The prime minister has said he will set out his case for military action to Parliament later this week but will only call a vote when he believes the government can muster enough support to win.
An influential Commons committee urged Mr Cameron earlier this month not to press ahead with a vote on UK air strikes.
But their intervention came before the deadly terror attacks in Paris, in which 130 people died, and the UN's subsequent decision to pass a resolution supporting action against Islamic State.
Some MPs' minds are said to have changed their minds so where do the parties stand?
The majority of Conservative MPs would vote to back extending UK air strikes against Islamic State targets in Syria.
Thirty Conservative MPs rebelled against David Cameron in August 2013, when the Commons rejected his first attempt to launch bombing raids on Syria - albeit against the Assad regime rather than IS.
A number of MPs who defied their party then - including Charles Walker and Andrew Bridgen - now say they will support the government, Mr Walker suggesting there was "no room for delay" in taking the fight to the extremists.
But about 20 Tory MPs are still expected to oppose any kind of intervention, arguing that bombing could be open-ended and will not help achieve a political solution to the civil war in Syria.
One of the rebels, John Baron, told BBC News British air strikes would have a "marginal effect" on the battle against so-called Islamic State and could "risk escalating the problem".
Total number of Conservative MPs: 331
Labour is split on Syria. Leader Jeremy Corbyn is firmly opposed to military action, arguing for greater efforts to find a "peaceful solution".
But some of his MPs, including members of his shadow cabinet, have said they would back air strikes if they had proper military and legal justification, including the approval of the United Nations.
They say the onus is on the government to come forward with a "comprehensive" strategy to stabilise Syria and to tackle extremism, demonstrating why it is in the UK's national interest to intervene.
About 20 to 30 Labour MPs are thought to be in favour of air strikes and willing to defy the party leadership over the issue. One of those, Mike Gapes, has said he is putting the interests of the country ahead of party by doing so.
Some MPs are pressing for what is called a free vote on the issue - where they won't be instructed to vote in a certain way. Shadow Chancellor John McDonnell suggested in the autumn this might be possible but Mr Corbyn has since seemed to rule this out.
Total number of Labour MPs: 232
The SNP opposed military action in 2013 but has many more MPs now and can exert real influence.
The party says it will listen to the PM's case for military action but remains "unconvinced" about the merits of the UK intervening.
Foreign affairs spokesman Alex Salmond told the BBC there was "no shortage" of countries bombing Syria at the moment. "Everyone and their auntie is bombing someone in Syria," he said. "What there is a shortage of is a coherent plan to bring about peace in Syria in a rapid timescale."
There should be more focus, he says, on disrupting Islamic State's communications and finances, asserting Western values to counter IS propaganda and preparing a long-term reconstruction plan for Syria.
Total number of SNP MPs: 56
Lib Dem leader Tim Farron has welcomed the UN resolution but indicated the government must do a lot more before counting on his party's support.
He has said David Cameron must reassure MPs there is a "broad coalition", including Russia, Turkey and Iran, working together on Syria and proper thought has been given to how Syria will be governed once Islamic State is removed.
Total number of Lib Dem MPs: 8
The Democratic Unionist Party, along with the SDLP and the UUP, helped to sink David Cameron's last attempt to launch air strikes in Syria, with five of its MPs voting against the move and three absent.
But DUP leader Nigel Dodds has suggested his party could take a different view this time around, saying he and his colleagues will "do the right thing for our nation's security, whatever that might entail".
Mr Dodds, who has said he expects to hold talks with the PM, has said any action must be realistic and effective to win his party's support and the prime minister must show he has learnt the lessons of the 2011 intervention in Libya.
Total number of DUP MPs: 8
Voted against military action last time and would be expected to do so again.
Total number of Plaid Cymru MPs: 3
UKIP's MP Douglas Carswell voted with the government in 2013, when he was a Conservative MP, despite expressing reservations about its lack of a "coherent strategy" in Syria. But UKIP has been consistent in its opposition to further military action.
The Green Party's MP Caroline Lucas voted against military action in 2013 and would be expected to do so again.
Party leader Natalie Bennett said the US-led bombing campaign, to date, had not reduced numbers of Islamic State fighters while the number of foreign nationals joining the extremist group had actually increased.
David Cameron has said it is his "firm conviction" the UK should join other countries bombing Islamic State militants in Syria.