Dominic Raab, the former Brexit secretary who triggered the current crisis by resigning on Tuesday, said he had been speaking "intensively" with Ms Leadsom and other ministers looking to change her deal.
May insisted she hasn't considered quitting as furious Conservative rebels try to gather the numbers to trigger a no-confidence vote.
The other is if 15% of Conservative MPs - now 48 - write letters saying they no longer have confidence in her.
Sir Graham told BBC Radio 5 Live that not even his wife knows how many letters he has received from other Conservative MPs.
"I have heard it said that this is like a football match, in which we are one-nil down at half-time, but as the Prime Minister suggested in her interview. we can still pull it back and get the Brexit we want", Johnson wrote in his weekly column for Monday's Daily Telegraph.
She also said she would be meeting European Commission chief Jean-Claude Juncker in Brussels ahead of the summit.
European Council President Donald Tusk has cast little doubt on the prospect of the deal being ratified, but has also said that "Brexit is a lose-lose situation, and that our negotiations were only about damage control".
British newspapers reported that five senior pro-Brexit ministers were working to pressure May to change the deal, but May said she saw no alternative plan on the table.
Tom Watson says it is time for Labour to be given a chance to rescue Brexit as he called for a General Election amid turmoil at the heart of Government.
"There is still more to be done and we do still have more time before the EU Council at the end of the month so I'm absolutely committed to getting the Brexit that 17.4 million people voted for", she added.
DeVos proposes overhaul to campus sexual misconduct rules
Rumors were circulating shortly after the midterm elections that DeVos was going to be stepping down from her position in January. Supporters said the rules would better ensure fairness in proceedings they believe have become too skewed against the accused.
May said Corbyn was "playing party politics" with Brexit.
Wendy Morton, Tory MP for Aldridge and Brownhills, has rallied behind the beleaguered PM, pledging her full support for her contentious Brexit deal. The November 25 event will see leaders of the remaining 27 EU states asked to put their stamp on the document, and the agreement will then be sent for ratification to both the Westminster Parliament and the European Parliament.
Mrs Braverman said: 'I do want the prime minister to continue but I want us to stick to the policies that were voted for in the referendum.
"I do think there is a point at which, we probably should have done it before, where we just say "I'm sorry this is the United Kingdom of Great Britain and Northern Ireland, we can not accept those dictated terms".
But some pro-Brexit Conservative MPs rallied against it because the United Kingdom will be in a customs union with the EU for years after Brexit, unable to sign meaningful trade deals with other countries, without the unilateral right to leave.
"There is still a margin to improve certain points and to clarify some of the measures, has said the british minister in charge of Relations with the Parliament, Andrea Leadsom".
He added that a deal should be demanded that would allow the country to leave the Customs Union unilaterally.
More than 20 have publicly said they have done so.
"If MPs (legislators) reject the deal, they will simply take us back to square one".
Leadsom told the BBC on Saturday that the deal needed improving and that the 'UK can not be trapped in a permanent customs arrangement.' Many are sceptical as to whether the European Union would make significant concessions if forced back to the negotiation table.