Commons Speaker John Bercow is expected to confirm that the amendment will be put to a vote, after the Opposition signalled it would not table a rival text.
Mr Cameron could also be challenged on the controversial issue at the weekly Prime Minister's Questions session.
Although the result is not binding on the government, it would be awkward for the premier to defy the will of the House.
Tory rebels said they believed 40 to 60 of their colleagues were ready to back the amendment, including Mark Reckless, Mark Pritchard, Zac Goldsmith, Bill Cash, John Redwood, Bernard Jenkin and Peter Bone. Many more could abstain.
However, some rebels questioned whether all Labour MPs would turn up to support the call.