The BBC, citing senior Conservatives, said MPs in the party have said they might back Mrs May's plan if she promises to stand down.
Britain's opposition Labour Party leader, Jeremy Corbyn speaks after tellers announced the results of the vote Brexit deal in Parliament in London, Britain, March 12, 2019, in this screen grab taken from video.
He said he told the PM: 'When I was told that we would have to come over and talk to you I began to cry.
It comes after the European Union announced that the original Brexit date of this Friday would be put back to May 22 if the deal is approved but only until April 12 if it fails once more.
However, after a disastrous last week, the increasingly isolated leader spent the weekend ensconced at her country residence Chequers "at the mercy of a full-blown cabinet coup", according to the Sunday Times.
Protesters descended upon the capital from up and down the United Kingdom to participate in the "Put it to the People" march, dubbed as one of the UK's largest, attracting an estimated 1 million people to demand that the British people are given another chance to vote on Brexit after MPs have failed to break the impasse over the issue in Parliament.
One cabinet minister is quoted as saying: "The end is nigh".
"To be talking about changing the players on the board frankly is self-indulgent at this time", Mr Hammond told Sky News's Sophy Ridge On Sunday.
Jet Airways chairman steps down as banks move in with rescue plan
The SBI-led consortium of lenders is working on a resolution plan for the cash-strapped Jet Airways for the last five months. Jet Airways, which is facing a severe cash crunch, defaulted on a domestic loan repayment in December.
"I'm realistic that we may not be able to get a majority for the prime minister's (Brexit) deal and if that is the case then parliament will have to decide not just what it's against but what it is for", he said. If she refused to go, ministers would threaten to resign.
Labour insiders know they can't win a no-confidence vote unless they have the DUP on side, and while the prime minister is racing around Europe trying to win concessions on the Northern Irish backstop they're holding their fire.
But on Friday night Mrs May wrote to parliamentarians warning if there is insufficient support for her Withdrawal Agreement in the coming days that she could seek an extension to Britain's EU membership beyond the European Parliament elections.
A million people took to the streets of London on Saturday to protest against Brexit and call for a second referendum that could reverse the decision to leave the world's largest trading bloc.
According to Tim Riddell, macro strategist at Westpac, the only Brexit certainty is continued uncertainty and with only a week before the Article 50 end date EU Leaders provided some breathing space for Mrs May's almost suffocated deal for a Withdrawal Agreement.
"Given that a second referendum is Labour Party policy, I was disappointed that Jeremy wasn't there".
Brexit Secretary Steve Barclay has warned that such a move could bring about a "constitutional collision" and increase the risk of a general election.