Former chancellor attacked the Prime Minister saying that she will never lead the party into another General Election after last week’s humiliation at the ballot box.
Mr Osborne said the Prime Minister was “dead woman walking” and could be ousted in a matter of days.
However, Graham Brady, the influential chairman of the Conservative backbench 1922 Committee, said there was no appetite for a leadership contest which could see the party having to fight another General Election.
Mr Osborne, who was sacked by Mrs May when she became Prime Minister and who now edits the London Evening Standard, said it was clear her days in Downing Street were numbered after seeing her Commons majority wiped out in the election.
“Theresa May is dead woman walking. It is just how long she is going to remain on death row,” he told BBC One’s The Andrew Marr Show.
“I think we will know very shortly. We could easily get to the middle of next week and it all collapses for her.”
Former cabinet minister Nicky Morgan, who was also sacked by Mrs May, predicted that there could be a leadership challenge over the summer.
“I think it’s fairly clear Theresa May cannot lead us into another election - of course, we don’t know when that’s going to happen, and I don’t think we should rush that,” she told ITV’s Peston on Sunday.
“But I do think if we’re going to have a leadership contest in the Conservative Party, what we cannot do is have another coronation like last summer.”
Asked about the timing of such a contest, she said: “Much to the upset probably of every journalist who was hoping for a summer off, I suspect it could be over this summer and I think it should involve our party conference as well.”
Former business minister Anna Soubry said Mrs May’s position was “untenable” in the long term but cautioned against a rush to replace her.
“I just can’t see how she can continue in any long-term way. I think she will have to go unfortunately. But not for some time,” she told Sky News’s Sophy Ridge on Sunday.
“We need stability, we need to put that sense of the economy and our country and the nation’s interests absolutely at the forefront, none of this messing about behind the scenes.”
Mr Brady said he did not believe there was any mood among Conservative MPs for a leadership contest that would create fresh instability.
“I think that there is zero appetite amongst the public for another General Election at the moment and I don’t detect any great appetite amongst my colleagues for presenting the public with an additional dose of uncertainty by getting involved in a rather self-indulgent Conservative Party election campaign,” he told the BBC’s Sunday Politics.
Mr Brady acknowledged there had been anger within the party at Mrs May’s failure to express any regret for the Tory MPs who lost their seats when she returned to No10 on Friday to announce she was carrying on at the head of a minority Government.
He confirmed that he had raised the issue with her before she gave an interview later that afternoon in which she said she was “sorry” at what had happened to them.
“Certainly one of the things I was very keen to press home was that in the past the Conservative Party has been very poor in its communications with colleagues who lost their seats in the general election. I certainly did say it is very important we did better this time,” he said.
Mr Brady said the loss of their Commons majority meant much of the party’s election manifesto would have to be abandoned and that Mrs May would have to present a “slimmed down” Queen’s Speech.
“There is no point in sailing ahead with items that were in the manifesto that we won’t get through parliament. I think we are going to have to work very carefully. I have no doubt that it will be a slimmed down Queen’s speech and we should concentrate on the bits that really have to be done,” he said.