The arrangements would see Scotland securing a Norway-style deal with the EU. The SNP leader is also expected to warn Westminster that if she fails to get the arrangement she wants, Sturgeon will call for a second Scottish independence referendum.
"Being part of the European Single Market is vital for Scotland's future economic wellbeing," said Sturgeon, according to the Press Association.
"And losing our place in the Single Market would be potentially devastating to our long-term prosperity, to jobs, investment and people's livelihoods.
"It would end our current status as part of the world's biggest free trade area, a market around eight times bigger than the UK's alone, and would have a profound and long-lasting impact on our national economic standing and our standards of living."
Prime Minister Theresa May reportedly phoned Sturgeon on Monday to tell the First Minister that she would look at the proposals "very seriously".
May has refused to give a "running commentary" on her Brexit negotiations, but the government will unveil a "plan" next year after MPs overwhelmingly backed a Labour "clarity" motion.
The Conservative premier has also promised to invoke Article 50, the official mechanism to split from the EU, before the end of March 2017.
Full speech from Sturgeon
I am pleased today to publish 'Scotland's Place in Europe' - a paper containing proposals to mitigate the economic, social, democratic and cultural risks that Scotland faces as a result of the UK wide referendum on EU membership in June.
Brexit is a problem not of Scotland's making.
And yet this is the first detailed plan for dealing with the implications of Brexit to be published by any government in any part of the UK.
As is well known, I believe Scotland should be an independent country - and as an independent country, that we should be full members of the EU.
The manifesto on which I was elected as First Minister, just 8 months ago, said this in relation to independence -
"The Scottish Parliament should have the right to hold another referendum...if there is a significant and material change in the circumstances that prevailed in 2014, such as Scotland being taken out the EU against our will."
I have made clear - and do so again today - that the option of independence must remain on the table.
Without this option, Scotland would simply have to accept the inevitability of whatever decisions the UK government makes, no matter how damaging they are to Scotland's interests.
That is not a position, in my view, that any politician or party should ever be content for Scotland to be in and as First Minister it is my duty to ensure that all options are open to Scotland in these unprecedented times.
However, independence is not the focus of the paper I am publishing today.
The day after the referendum in June, I made a clear commitment.
I promised to explore - not just my preferred option of independence - but all options to protect Scotland's place in and relationship with Europe.
I said specifically that we would seek to find a solution that would enable Scotland's voice to be heard and our interests protected from within the UK.
This paper fulfills that commitment.
Indeed it goes further and sets out ways forward that I believe would be in the interests of the rest of the UK as well.
'Scotland's place in Europe' sets out proposals to keep Scotland in the European single market, and to equip the Scottish Parliament with the additional powers it needs to serve and protect Scotland's interests in the post Brexit landscape.
Now, let me be clear: these proposals fall short of what we consider to be the best option for Scotland and the UK - full membership of the EU.
So far from setting a high bar for the UK government, they represent a significant compromise on the part of the Scottish Government.
They are a serious and genuine attempt to build as much consensus as possible - to square the circle, if you like - and to unify the country around a clear plan to protect our interests.
I hope and expect that the UK government, in considering our proposals, will demonstrate the same flexibility and willingness to compromise.
Let me turn now to the detail of the paper.
It sets out why keeping our place in the single market matters so much.
It matters principally to our economy - to jobs, trade, living standards and investment.
It is estimated that being outside the single market could cost the Scottish economy 80,000 jobs. Workers could lose £2,000 a year within a decade of a hard Brexit.
Being in the single market also ensures protection for workers' and consumer rights.
It facilitates the flow of skills that our economy depends on and allows all of us to travel, work, study and live across Europe if we so wish.
It will guarantee the rights of EU citizens already living here.
And it provides a platform for co-operation on some of the major issues of our times, like climate change.
So the paper sets out the primary ways in which Scotland's place in the single market can be protected. It has three main strands.
Firstly, we propose that the UK as a whole should stay in the single market - by remaining a party to the European Economic Area Agreement - and that it should also stay in the customs union.
Membership of the EU and of the single market are two distinct propositions - as the position of three of the four EFTA countries demonstrates.
I accept that there is a mandate in England and Wales to take the UK out of the EU. However, I do not accept that there is a mandate to take any part of the UK out of the single market.
It would make no economic sense whatsoever for the UK to leave the Single Market. And it would be entirely democratically justifiable for the UK to remain within it.
So the Scottish government will continue to argue - and build common cause with others of like mind - for continued UK membership of the single market.
However, I reluctantly accept that as things stand - given the rhetoric of the Conservative government - that seems an unlikely outcome.
The Tories seem intent on placing a higher priority on cutting immigration than on anything else - the economy, jobs and living standards all lag behind on their list of priorities.
As a result, the second strand of this paper proposes ways in which Scotland could stay in the single market - through EFTA and the EEA - even if the rest of the UK chooses to leave.
The paper does not shy away from the challenges associated with such an option.
In fact it specifically identifies the key challenges - for example, how continued membership of the single market could be achieved without Scotland being an independent country; the legislative and regulatory requirements; the issue of financial contributions; and the practical implications around free movement of goods, services and people - and it sets out the basis of how each of these challenges could be overcome if the political will exists to do so.
It is also important to note that this option does not prioritize membership of the EU single market over continued free trade across the UK. It would safeguard both.
Talk of a hard border for Scotland has always rung hollow from a UK government that says no such hard border will be required between a post Brexit UK and the Republic of Ireland, a continuing member of the EU.
But that argument aside, this paper sets out how free movement of goods, services and people would continue across the UK, even with Scotland in the single market and the rest of the UK not.
In that respect, it is worth emphasizing that what we propose would not see Scotland having a different relationship with the customs union to the rest of the UK.
We hope the UK will stay in the customs union. If it does so, then this proposal would enable Scotland to be in both the single market and the customs union.
However, if the UK opts to leave the customs union, then Scotland - in common with other EFTA EEA countries - would not be in the customs union either.
There will of course be disadvantages to Scottish businesses if we are not in the customs union - although those disadvantages would be minimized if Scotland remains in the single market.
However, under this proposal the border between Scotland and England would not be an external EU customs border. What is in effect a customs union now between Scotland and the rest of the UK would continue.
There will be those who say a differentiated option for Scotland such as the one we propose would be too difficult to achieve - and as I have said, the paper does not underestimate the challenges.
However, it is important to consider these three points.
Firstly, there are already a range of asymmetric and differential arrangements in operation within the EU and single market framework.
The solution we seek for Scotland would be different in detail and scale to many of those arrangements, but not different in principle.
Second, the UK government already appears open to a 'flexible Brexit' approach in relation to different sectors of the economy. It will also be necessary to take a flexible approach in relation to Northern Ireland and Gibraltar. There is no good reason why such flexibility should not also apply to Scotland.
And lastly, and perhaps most fundamentally, everything about Brexit will be difficult and unprecedented. The negotiations ahead will be characterized by a need to find practical solutions to a range of complex issues. It is in that spirit that we seek to find solutions that will respect the voice and protect the interests of Scotland.
The final strand of the paper deals with the powers of the Scottish Parliament.
It argues that in light of the removal of rights and responsibilities provided by EU law - and whatever the outcome of the Brexit negotiations - Scotland's interests within the UK demand that the devolution settlement be fundamentally revised.
The paper looks at three broad categories of powers that must now be considered.
Firstly, powers to be repatriated from the EU which currently sit within Scottish Parliament responsibility - for example, fishing, the environment, justice and agriculture. These must remain within devolved competence. There must be no Westminster power grab.
Secondly, powers to be repatriated that are not currently devolved but which would enable the Scottish parliament to protect key rights - for example, employment law and social protection.
And, thirdly, a broader range of powers to protect Scotland's interests and support a differentiated solution of the kind proposed in this paper - for example, power over immigration.
In short, the proposals in this paper are detailed, serious and reasonable. They are designed to respect Scotland's voice and protect our interests, whilst also acknowledging the position the UK finds itself in.
Let me now, briefly, set out how we intend to take these proposals forward.
We accept absolutely that the negotiation that will start on the triggering of Article 50 will be between the UK and the EU.
These proposals are therefore aimed, first and foremost, at the UK government.
We want the UK government to make clear when it triggers article 50 that it intends to stay in the single market and the customs union.
If it will not do so, we want the U.K government to seek, as part of its negotiation, a differentiated solution for Scotland as set out here.
We will submit these proposals to the UK government through the Joint Ministerial Committee framework for discussion in the new year.
The prime minister, when I met her in this room in July, pledged to fully and fairly consider the proposals we brought forward.
She repeated that commitment when I spoke to her on the phone yesterday morning and I welcome that.
It is beyond any doubt that the Brexit vote - with its different outcomes in different parts of the UK - has raised fundamental questions, not just about our relationship with Europe, but also about how political power is exercised across the UK.
So to the Westminster government, I say this - your response to these proposals will tell us much, perghaps everything, about whether the UK is, in reality, the partnership of equals you claim it to be.
To our European partners, I today reaffirm our belief in, and commitment to, the core values of solidarity, co-operation and democracy that underpin the European Union.
And to the people of Scotland I pledge this: I will continue to do everything I can to protect your interests as we navigate the challenging times ahead.