The UK prime minister, in New York for a UN General Assembly meeting, will be holding talks about “what more the UK can do to contribute”, No 10 added.
The UK is already providing arms to the Kurds as well as surveillance support.
The BBC’s Nick Robinson said Parliament could be recalled by Friday if Labour and Lib Dems back UK military action.
The involvement of UK forces could be restricted to Iraq, where they would be operating at the invitation of the government in Baghdad.
Nick Robinson said Mr Cameron would only put the issue to a House of Commons vote, if he was confident of support from Labour, the Lib Dems and his own backbenchers.
“David Cameron will not risk a repeat of the Commons defeat he faced last summer over air strikes in response to President Assad’s use of chemical weapons.”
‘ Fair wind’ for action:
Former Labour foreign secretary Jack Straw said under the right circumstances there could be support for Britain joining air strikes in Iraq.
He said the situation was different from when the Commons voted against intervention in Syria last year.
“If Mr Cameron comes to Labour and there’s a clear proposition I think he’ll get a fair wind,” he said.
Several Conservative MPs who opposed air strikes in Syria last summer have told the BBC they would now support military action.
Crispin Blunt, a former minister and one of the Tory rebels at the time, said there was “no great controversy” about the UK’s military involvement – short of a significant ground commitment – and there was no need to recall Parliament.
“Any military strategy against ISIS, which is necessary, must involve taking them on in Iraq and Syria,” he said.
Another of last year’s Tory rebels, Sarah Wollaston, said if Syrian strikes were the only way to hit IS effectively she would support them.
She has explained her position in an open letter to constituents on her website.
Conservative Julian Lewis said he “would be in favour” of military action if there was “a coherent and sensible plan”.
Another backbencher who rebelled last year, Charles Walker, said he would support action against IS with or without the recall of Parliament.
Other Conservatives have privately confirmed they would support strikes.