George Osborne has branded the Prime Minister "a dead woman walking".
In a withering attack on Theresa May, who sacked him as chancellor on her arrival in Downing Street last year, Mr Osborne said it was simply a question of "how long she is going to remain on death row".
He predicted she could be out of office as early as the middle of next week.
Tory MP Anna Soubry also said Mrs May's position in the long-term was "untenable", but argued she should not quit now because of the need for stability.
Ms Soubry told Sky News' Sophy Ridge on Sunday programme: "She will have to go, but not for some time."
The speculation over the PM's future came as she moved to shore up her precarious position following the loss of her Commons majority at the election.
However, this was dealt an early blow after Downing Street mistakenly announced a deal had been reached with the Democratic Unionists to prop up Mrs May's minority Tory government.
Meanwhile, Jeremy Corbyn, buoyed by Labour's showing at the polls, said it was "quite possible" there would be another election this year and that his party was "ready to fight".
Earlier, Mr Osborne, who is now editor of the London Evening Standard, told BBC1's The Andrew Marr Show: "Theresa May is dead woman walking. It is just how long she is going to remain on death row.
"I think we will know very shortly. We could easily get to the middle of next week and it all collapses for her."
Asked what he thought of Mr Osborne's comments, former Tory leader Iain Duncan Smith said: "I don't think anything at all of what George Osborne says. I make it a rule."
Defence Secretary Sir Michael Fallon said he and other senior colleagues had told the PM she would need to adopt a more collective approach after seeing her majority swept away.
He welcomed the resignation of Mrs May's closest advisers, Nick Timothy and Fiona Hill, who faced criticism over the election fiasco.
Mr Fallon told Marr: "Clearly a minority government requires a different approach.
"We have already seen some changes in personnel in Downing Street. I welcome that.
"We are going to see, I hope, more collective decision-making in Cabinet. I and other senior colleagues have made that clear to her.
"And I think you will also see that she will want to work much more closely with the parliamentary party, both in the conduct of business and in the development of policies."
Asked on Marr if there will be another general election this year, Mr Corbyn said: "I think it's quite possible there'll be an election later this year or early next year, and that might be a good thing because we cannot go on with a period of great instability.
"We have a programme, we have support and we're ready to fight another election campaign as soon as may be, because we want to be able to serve the people of this country on the agenda we put forward, which is transformative and has gained amazing levels of support."
Shadow cabinet member and key Corbyn ally Emily Thornberry said Mrs May was "squatting in Downing Street".
She told Sky News: "Our manifesto is popular, our vision for Britain is right, they have no idea of what they are doing, we are waiting in the wings, we will step in if we are required and called upon to serve."
Labour MP and former shadow home secretary Yvette Cooper told Sophy Ridge: "We have got to keep challenging Theresa May and this deeply dodgy DUP deal.
"Theresa May held a referendum on herself and lost it so the idea that she can just carry on as if the election didn't happen simply through this dodgy deal... is not on."
She added: "I think we are going to have to prepare for another general election because while I don't think it's what a lot of people want... I just don't see that what Theresa May is doing is sustainable, so therefore we have to be ready for whatever comes at us."
Speaking to Sky News, former Conservative deputy prime minister Lord Heseltine said of the PM: "She'll never lead the Conservative Party into another election.
"But there's no immediate need for a change. Indeed my own hope would be that perhaps her last service to the party would be to give it the time to think about a successor but very much in the context of the policies of the successor.
"You have got to face the reality that the present situation is unsustainable. The DUP may be a short-term palliative but it's not enough of a support to last through a Parliament.
"What the Conservative Party has to ask itself very simply is: 'How do we stop Jeremy Corbyn entering Number 10 Downing Street?'"