David Davis says Theresa May will lose Tuesday’s vote on her Brexit deal and be forced to return to Brussels for further talks until she gets an acceptable agreement.
Speaking to Sky News, the former Brexit secretary said the deal would be rejected because it meant Britain would become a "rule-taker".
His comments came as Tory MP Will Quince quit the government over Mrs May's deal, and Work and Pensions Secretary Amber Rudd warned of "chaos" if it is voted down.
Mr Davis said: "I don't think [Mrs May] win.
"I think that the deal will be rejected because it's seen by everybody to leave us as rule-takers, to leave us as a subordinate and not actually answer the questions or meet the promises either in our manifesto or in the referendum.
"I think she'll go back to the EU, I think they will talk to her. Hopefully they will have substantive talks, we have lots of ideas of the sorts of things they could do to improve were we are now.
"The outcome of that is that she'll have to come back to parliament again and hopefully this time with a deal we will accept."
Resigning from his role as ministerial aide to Defence Secretary Gavin Williamson, Mr Quince said he could not accept the deal as it stands.
Writing in the Sunday Telegraph, he said: "Unless the backstop is addressed to include either an end date or a unilateral exit mechanism, I cannot support it and so am resigning from the government as a Parliamentary Private Secretary".
Earlier, Ms Rudd warned that "anything could happen" if the UK-EU agreement is turned down, "most of which they won't want to happen".
MPs needed to consider if they preferred the alternatives, including the softer Brexit Norway-style option or another referendum that risked reversing the 2016 result, said Ms Rudd.
She acknowledged Tuesday's vote was "going to be difficult", but was adamant Mrs May would remain as prime minister even if her government was defeated, insisting "she will see us through this".
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".
Ms Rudd became the first cabinet minister to publicly discuss a "Plan B" if Mrs May's deal was rejected.
The Remain-supporting frontbencher said a so-called Norway-plus model was a "plausible" alternative.
This option would be particularly unpalatable to Brexit backers as it would see the UK remain closely tied to the EU, inside both the single market and a customs union.
Supporting the withdrawal agreement secured by the PM, Ms Rudd said: "I think this is the right deal for the country.
"I think it will get through but I know it's going to be difficult, because of people are still declaring against it."
She added: "The point about me discussing other alternatives is to remind people that it is all very well saying, 'I don't like this about the agreement or I don't like that about the agreement.'
"What happens if it's voted down? Anything could happen. There's lots of different things that could happen, most of which they won't want to happen. So when they think about this deal they need to weigh up the alternatives as well."
Ms Rudd argued there was "a lot of support" for the Norway-plus model in the Commons and a "certain amount of support" for a people's vote.
She said: "People should think very clearly if they are not going to vote for the Government's withdrawal agreement whether they would actually prefer those alternatives.
"The withdrawal agreement we have will deliver the stability that we want, that our businesses need, the investment that we want."
On the Tory leader's future if the agreement was voted down, Ms Rudd said: "Theresa May is a prime minister who will stay through this. I am absolutely convinced. I know that she will see us through this."
And in a warning to colleagues mulling a challenge for the top job, she said: "We are in difficult 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.
"Nobody knows what happens next and that chaos needs to be avoided."
Her comments came as critics said Mrs May could be forced to stand down if her deal was defeated.
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".