If this pans out, the risk of a no-deal Brexit and the chaos that would bring with it, increases.
Earlier, on November 14, May announced that her Cabinet had approved a Brexit deal.
The Work and Pension's Secretary's claim has provided momentum to the campaign to get a similar deal to the Norwegian model after she said the alternative seemed "plausible not just in terms of the country, but in terms of where the MPs are".
"I will certainly not be voting to hand over £39bn to the European Union with nothing in return in a deal which keeps us shackled to the European Union in perpetuity".
Mr Davis said: "I don't think [Mrs May] win".
She was discussing the merits of a "plan B" in an interview with the Times on Sunday, but said she still supported Mrs May's deal which will be put to a vote on Tuesday.
The Conservative frontbencher also took a swipe at colleagues rumoured to be plotting leadership bids behind the scenes, arguing a contest would "add another layer of difficulty" to an already challenging situation and be "a real mistake".
What is the Norway model?
Overall, it found that the option of staying in the European Union had the largest single support, with backing from 46 per cent of people.
For all the people in Northern Ireland, this means continuing the progress over the past two decades under the Belfast Agreement, supporting our business community to thrive, ensuring a good deal for our agricultural and fishing industries and providing a safe, secure and prosperous society for future generations. I think because I was a Remainer I feel it's a very hard job to deliver.
"What happens if it's voted down? So when they think about this deal they need to weigh up the alternatives as well".
There are many possible outcomes of debate, including a "no deal" Brexit, a second vote, renegotiation or a new general election.
Theresa May needs 320 votes in Commons to approve the European Union withdrawal agreement.
"The withdrawal agreement we have will deliver the stability that we want, that our businesses need, the investment that we want".
The Cabinet minister also appeared to endorse an amendment to the Government's motion for the vote on Tuesday tabled by former Northern Ireland minister Sir Hugo Swire in an attempt to win over wavering Eurosceptics. I am absolutely convinced.
(We know you cheated).
And in a warning to colleagues mulling a challenge for the top job, she said: "We are in hard times at the moment to add another layer of difficulty by having those sort of conversations would be a real mistake and would not be in the national interest".
The vote is expected to lead to the possibility of a No-Deal Brexit, as plenty of MPs have indicated that they could vote against the PM's agreement with Brussels.
Eurosceptic former party leader Iain Duncan Smith cautioned against the PM and her Cabinet deciding to "brazen it out", saying such an approach would be a "disaster".
DUP leader Arlene Foster has said a Commons amendment supported by backbench Tories giving Parliament a say on invoking the Irish border backstop does not go far enough, adding that domestic "tinkering" to the Withdrawal Agreement would not persuade her party's ten MPs to back the government.
"If we go into government straight away we would start negotiating straight away".
Mr Corbyn said his party was ready to "step in and negotiate" with the European Union and would form a minority government "if that is what is on offer".
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