The Prime Minister would hand over control of the trade deal phase of Brexit talks to a Leave supporter in return for Brexiteer rebels agreeing the current divorce.
The idea has been proposed by Gavin Barwell, Mrs May’s top aide, and been discussed with at least two Cabinet ministers, the Sunday Times said.
Mrs May has not signed up to the timetable but amid revolt over he deal before Christmas did accept she would quit ahead of the 2022 election.
The Prime Minister must set out an outline of her Plan B Brexit in the Commons tomorrow and will speak to her Cabinet on a conference call this afternoon.
She faces two different plans from fractious backbenches to freeze out the Government and let MPs take over Brexit talks.
Trade Secretary Liam Fox warned the plotters today that if they succeed in stopping Brexit it would unleash a ‘political tsunami’ with ‘unknowable consequences’.
Theresa May (pictured with husband Philip attending church today) could offer to resign as soon as May to get Brexit deal through Parliament under plans being promoted by her chief of staff, it was claimed today
Trade Secretary Liam Fox (pictured leaving Parliament on Wednesday night) warned the plotters today that if they succeed in stopping Brexit it would unleash a ‘political tsunami’ with ‘unknowable consequences’
A source told the Sunday Times, the Prime Minister offering to quit in May or June was being discussed by her team.
It would allow for an orderly Brexit and give time for a Tory leadership contest – but end hopes of Mrs May shaping a post-Brexit legacy.
The source said: ‘The response came back that while the chief herself had not thought about it, the team around her had.’
Dr Fox wrote in the Sunday Telegraph today that those on the opposite side of the debate must not cancel Brexit.
He adopted Mrs May’s warning that last week’s devastating defeat of the deal must move on and the Rebels must ‘tell us what they do want’.
Dr Fox said: ‘Failure to deliver Brexit would produce a yawning gap between Parliament and people, a schism in our political system with unknowable consequences.
‘The reaction of the Question Time audience could become a political tsunami. It is time for MPs to deliver on the promises they made.
‘It is a matter of honour and a matter of duty.’
The idea has been proposed by Gavin Barwell (left with Michael Gove in Downing Street on Thursday), Mrs May’s top aide, and been discussed with at least two Cabinet ministers
Amid the warnings, a senior Cabinet minister told the Sunday Express Work and Pensions Secretary Amber Rudd, justice secretary David Gauke and Business Secretary Greg Clark back a second referendum
The minister said: ‘They would do anything to stop Brexit.’
The minister added: ‘The fear is that Labour will pivot to supporting a second referendum.’
The minister also accused Brexiteers of ‘overplaying their hand’ and warned that the likelihood is that Parliament and the Government will ‘go for something softer’.
The minister went on: ‘I think if there is a majority view in the Cabinet it is that we commit to a customs union of some sort and I suspect that is where we will end up.
‘The Cabinet in some ways reflects the party over not being clear which way to go except we don’t have any [Brexiteer] hardliners any more. Penny [Mordaunt] and Andrea [Leadsom] are much more pragmatic Brexiteers.
‘We have legislation which will have to go through and that can be amended to stop no deal and to have a second referendum.’
Labour MP Rupa Huq, a supporter of the Best for Britain campaign, said: ‘The Prime Minister can make the ultimate sacrifice if she wants but it won’t make her bad Brexit deal any better.
‘At the moment she is in office and not in power. But I do have to say the idea that her Chief of Staff is running round telling the cabinet, half of whom are openly plotting to take her job, that she has go is just awful. It looks like the ultimate betrayal.
‘This plotting shows why we need to go back to the people.’