It comes as EU leaders suggest the leave date could be pushed back beyond March if she loses.
At least three Cabinet ministers are believed to be trying to persuade the PM to put the December 11 vote off.
Labour plans to issue a vote of no confidence if May loses.
According to the Daily Mail, one said: "We need to be creative and we need to get the D
UP back on board. It can be done, but it can't be done before next Tuesday."
Another said: "Marching people into the valley of death next Tuesday is a mistake."
May is trying to salvage her deal and win over Conservative dissenters by offering a "lock" on the Northern Irish backstop – giving MPs final say on the arrangement.
She could also unveil a new law marrying Northern Ireland's rules to the rest of the UK during a backstop period.
But with the clock ticking, and unrest across Parliament, some senior Tories have suggested she delay the vote.
According to the Telegraph, EU leaders would offer her a chance to extend the Article 50 deadline if she is voted down in the Commons next Tuesday.
It could give Britain more time to negotiate a deal before the March 29 axe falls.
Downing Street has always ruled out a date change.
Senior Tories on both sides of the Brexit divide predicted Britian’s EU departure date of March 29 will now be delayed as ministers will be forced to put together a new softer option to please Parliament.
Last night there was fury as a growing number of Tory rebels backed Labour in a coup to inflict the landmark defeat on the Government.
International Trade Secretary Liam Fox blasted it as a plot to “steal it Brexit the British people”.
May's chances of winning next Tuesday's vote was handed a fresh blow after documents proved her deal risks splitting Northern Ireland from the rest of the UK “indefinitely”.
The DUP, which props up her administration, warned her leadership could be over if she ploughs on with the plans.
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