The constituency is likely to become one of the key target seats for Labour, with Rudd, a potential successor to May, wielding a wafer-thin majority of just 346. This makes Rudd vulnerable to a "decapitation" strategy that could see Labour throw vast resources at the constituency to unseat a possible future Tory leader.
A source close to Corbyn refused to confirm the timetable but acknowledged there were "arguments for doing it then".
Julian Smith, the Government's Chief Whip, has warned Tory MPs that a confidence motion could be "tabled on [Thursday]", telling them to "prepare accordingly".
Corbyn could ask his MPs to either abstain or vote against an amendment put forward by Hilary Benn, the Labour backbencher, amid fears it will damage the prospects of the censure motion succeeding. That amendment, if passed, would reject the Withdrawal Agreement, convey a lack of support for no-deal and pave the way for alternative plans for Brexit.
However, Corbyn's team are opposed to it because it would allow May to pull the vote on her Brexit deal, thus sparing her a crushing defeat.
A party insider confirmed that Labour had "gone cool" on the amendment, adding that Corbyn was focused on defeating May's deal.
Doubts remain as to whether Corbyn can secure enough votes for the motion from Tory rebels or the DUP.
If he is unable to force a snap election, Corbyn will come under greater pressure to throw his weight behind a second referendum, an option he has repeatedly played down.