MPs must be given "a straight up-and-down vote" on the PM's Brexit deal later, No 10 says, but it is not clear whether the Speaker will allow it.
John Bercow is due to announce his decision at about 15:30 BST.
The PM tried to bring his deal to the Commons for a vote on Saturday, but his strategy was dealt a blow when MPs backed moves to delay approval instead.
The Speaker has previously ruled out repeatedly bringing back votes on the same matter more than once.
BBC assistant political editor Norman Smith said Mr Bercow looked set to reject the PM's demand.
Following Saturday's special sitting, and under the Benn Act, Boris Johnson was forced to send a letter asking the EU for an extension to the Brexit date - although he did not sign it.
Brexit legislation
Mr Johnson reached a new deal with the EU last week, but it needs to be approved by the UK Parliament - he wants MPs to say a clear "yes" or "no" to that on Monday afternoon.
The legislation which would implement Brexit - called the Withdrawal Agreement Bill (WAB) - will also be introduced on Monday and must begin the process of parliamentary scrutiny.
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