The Defence Secretary Michael Fallon is expected to tell MPs in Parliament today (2 July) that parliament should consider attacking the forces of Isis not just in Iraq but also in Syria.
He is expected to say that there is no legal barrier to British military attacks, noting that both the Canadian and Jordanian air forces have already attacked Syrian targets.
Fallon is expected to ask parliamentarians to reconsider the arguments on military action in Syria. In August 2013, Prime Minister David Cameron failed in his attempt to win support for airstrikes on Syrian government targets designed to deter the use of chemical weapons.
His comments will be seen as the clearest sign that the government is considering increasing military action in the Middle East to fight terrorists.
BBC reports that Fallon will repeat Cameron's assurance that there will be no military action in Syria without another vote in the House of Commons.
Britain's Royal Air Force has been carrying out strikes in Iraq since September but the government is now re-considering the case for similar missions in Syria, BBC said.
The Telegraph quoted Fallon as saying that it was "illogical" for Britain to take part in bombing campaigns against Isis in Iraq but not in Syria.
He told BBC Radio 4: "It is a new Parliament and I think Members of Parliament will want to think very carefully about how we best deal with Isil [Isis] and the illogicality of Isil not respecting the borderlines.
"They don't differentiate between Syria and Iraq, they are establishing this evil caliphate across both countries," he said.
Fallon will tell MPs that there is a possibility that the murder of up to 30 Britons in Tunisia on 26 June by student Seifeddine Rezgui, 23, may have been planned in Raqqa in Northern Syria.
Following the attack, Cameron said that Isis posed "an existential threat" to the West and its members in Iraq and Syria were plotting "terrible attacks" on British soil.
BBC said that the Conservative government would not risk losing another vote Syria unless they are assured of the support of the Labour Party. It is understood that both parties have been in touch to discuss the possibility of another vote on Syrian military action, although nothing is expected imminently, BBC said.