Speaking to the BBC, the chancellor said a "short extension" to Article 50 - the mechanism that allows the United Kingdom to leave the European Union - was necessary to enable the government to pass all the legislation required to enact Brexit.
But it is thought the Prime Minister could delay the crucial vote for another week unless she is confident of avoiding a third humiliating defeat on the package, which MPs rejected by 230 votes in January and 149 last week.
Further talks are expected over the coming days with the DUP in the hope that persuading the ten Northern Irish MPs to back the deal will help sway scores of Tory Eurosceptics to fall into line.
"The reality is that practically, to get it signed off by all parties, we would have had to have a deal concluded by today to get it through before Thursday's European Union council", said a source.
Asked if the deal would be voted on again this week, the chancellor said: "The answer to that is no - not definitely".
The Labour leader has invited Liberal Democrat leader Sir Vince Cable, DUP deputy leader Nigel Dodds, SNP Westminster leader Ian Blackford, Plaid's Liz Saville Roberts and Green MP Caroline Lucas.
It has been reported by the Spectator magazine that there is a "better than 50:50 chance" the party will support the deal next week.
According to precedents stretching back to 1604, parliamentary rules say that substantially similar proposals can not be voted on in the House of Commons a couple of times during the same session of parliament.
Earlier, former foreign secretary Boris Johnson called on Mrs May to postpone another vote on her deal, warning it would be "absurd" to bring it back to the Commons without first securing change from Brussels.
Q&A What does the Speaker's ruling on a third meaningful vote mean?
If, however, Mrs May puts her deal to a vote and wins, she will ask for an extension to Article 50 up to June 30 to prepare the legislation for Brexit. Prime minister Theresa May would have to make "substantial" changes to her government's two previous attempted to pass the withdrawal agreement deal with the EU.
"This is my conclusion: if the government wishes to bring forward a new proposition that is neither the same, nor substantially the same, as that disposed of by the House on the 12th of March, this would be entirely in order", Bercow said.
"What the government can not legitimately do is resubmit to the house the same proposition, or substantially the same proposition", he said, citing precedent dating back to 1604.
He also told Sky's Sophie Ridge that Labour MPs could be told to vote in favour of an amendment calling for another referendum next week, and he could propose another vote of no confidence in the government if the PM's deal was voted down for a third time.
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"A two-year extension is basically remaining in the European Union".
Northern Ireland's DUP leader Arlene Foster speaks to the media outside Stormont Parliament Building in Belfast, Northern Ireland February 6, 2019.
Other ministers involved in the talks included David Lidington, Michael Gove and Julian Smith, he said.