The newspaper cited "ministers and aides" who said they expected her to announce on Sunday that she was delaying the vote.
But her position appears precarious, with potential rivals on manoeuvres in case she is ousted or quits.
The Prime Minister has repeatedly stated the so-called "meaningful vote" in Parliament would go ahead as scheduled despite threats of resignation. "The risk is that we don't have Brexit or we don't have a deal".
Theresa May will push ahead with a crucial vote on her European Union exit deal, her Brexit minister said on Sunday, as senior lawmakers in her own party piled pressure on the British prime minister to go back to Brussels and seek a better offer.
Mr Farage also suggested Mrs May could have to head off to Brussels once more to plead European Union leaders for further concessions should her Brexit agreement be shot down on Dember 11.
Defence Secretary Gavin Williams' parliamentary aide, Colchester MP Will Quince, also quit on Saturday over the Irish backstop issue.
Johnson warns of EU 'blackmail' risk under May's Brexit deal
Barclay said Britain would enter "uncharted waters" if it loses the vote, but May could stay on as prime minister.
Cabinet minister and Breixteer Penny Mordaunt said to be deciding whether to back the deal or quit the Cabinet. Parliament looks likely to reject the deal in a move that threatens to bring down Mrs May's government.
"The vote is going ahead because it's a good deal and it's the only deal", he said, adding that MPs should allow "the ideal to be the enemy of the good".
Asked to give an "absolute, categorical promise" that he would not stand against the Prime Minister, Mr Johnson told the BBC's Andrew Marr Show: "I will give you an absolute, categorical promise that I will continue to advocate what I think is the most sensible plan".
Former attorney general Dominic Grieve suggested that the Tory party could split over Brexit.
Labour is considering its options if Mrs May is defeated and would hold talks with other opposition parties about how to proceed.
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