Leader Jeremy Corbyn will make it clear that the party's official policy is to oppose the military action, but will not impose a whip directing them to vote against.
Christian Labour MP Rachael Maskell told Premier's News Hour members should listen to leader Jeremy Corbyn's position.
She said people would be "very wise" to pay attention to his views.
"He's a party leader who probably has more experience of global affairs than any leader of any party ever has.
"He has asked some very pertinent questions of the prime minister of which he has received some answers but not all.
"Therefore I think it's important to weigh what he is saying against what the prime minister is saying and that's the role of the leader of the opposition.
"I think he's doing an excellent job in challenging the prime minister over what he's proposed and I know he will continue to do so."
A free vote would clear the way for Mr Cameron to call a vote on air strikes as early as Wednesday with confidence that he will obtain the "clear majority" which he has said is needed.
But it is thought that Mr Corbyn may appeal for the Prime Minister to delay a vote while the concerns of Labour MPs are dealt with.
Mr Corbyn has written to Mr Cameron urging him to allow a full two days of debate on the air strikes proposal.
In his letter, the Labour leader said: "In the view of the Opposition on a matter of such critical importance there must be full and adequate time for any debate in the House and only a full two-day debate would ensure time for all members who wish to participate to be able to do so.
"As has happened previously a one-day debate would inevitably lead to important contributions being curtailed. It is incumbent on us all to ensure the country feels there has been the fullest parliamentary discussion of what you have rightly described as a highly complex situation."
Ms Maskell, the member for York Central, said suggestions some Labour MPs could be using the Syria debate as a way to get rid of Jeremy Corbyn "despicable".
"I believe the matter before parliament has got to be given the focus and the attention and therefore politics doesn't come into this," she said.
A Number 10 spokesman said discussions were under way within government on the wording of a draft motion - covering not only military action but also work on counter-extremism, the diplomatic and political process and the ongoing humanitarian effort - but stressed there was so far no timetable for it to be put before MPs.
Downing Street confirmed MPs from all sides of the House were being offered briefings on the Government's case for UK involvement in air strikes.