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, Boris Johnson was forced to send a letter asking the EU for an extension to the Brexit date - although he did not sign it.
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.
Labour's shadow Brexit Secretary Keir Starmer has said his party will push for changes when the bill is brought to Parliament, for example, demanding a UK-wide customs union with the EU and single market alignment, and backing moves to put the deal to a referendum.
The DUP has so far refused to support Mr Johnson's deal - and Labour has attempted to reach out to it - but the Northern Irish party's chief whip, Jim Shannon, told Sky News a customs union was "something that we cannot support and will not support".
He said the party was meeting to discuss its strategy, but added: "I believe that will be the stance we will have later on when we see the wording."
The prime minister's spokesman has reiterated the government's opposition to a customs union and another referendum, saying: "Both of those have been voted on on a number of occasions in the House of Commons and neither have been successful."