Theresa May will urge EU leaders to adopt a more "sustainable" plan to tackle the continent's migration crisis when they meet in Brussels on Thursday (15 December).
The British prime minister will also urge her European counterparts to have a "greater engagement" with Egypt, according to a Number 10 source.
"[A sustainable footing means] having an approach on migration that means countries across Europe can deal with this in a sustainable way," the source said.
"So, rather than the focus just being on how do you deal with the numbers arriving at Europe's borders, actually having a much better plan and effort to reduce the numbers arriving at Europe's border by looking at using the relationships with other countries that you have."
The source said May wanted to highlight the importance of Egypt because the country has been a "big source" of unaccompanied minors to the EU.
But a Turkey-EU-style migration deal is "not on the table" for Egypt at the EU Council.
The Number 10 course claimed the Turkey-EU agreement has seen the number of migrants travelling to the EU via the Aegean Sea drop by 95% since it formally came into force in March 2016.
For the UK's part, May is expected to announce that the Home Office will send 40 extra staff to Greece to help with asylum claims. The additional immigration officials will start to be sent to Greece from January 2017 in two eight-week-long phases.
Elsewhere, the other 27 EU leaders are expected to hold an informal dinner on the night of the summit, where they will discuss Brexit negotiations.
May's official spokeswoman has previously described the move as "reasonable", but stressed any business affecting the whole of the EU should be discussed by all of the bloc's leaders.
The British prime minister had promised to trigger Article 50, the official mechanism to split from the EU, by the end of March 2017.
The move will start formal negotiations between the parties, while the European Commission's chief Brexit negotiator Michel Barnier expects a deal to completed by October 2018 and ratified by the end of March 2019.