Philip May will ask the Prime Minister to stand down instead of risking public humiliation, The Sun reported. Mrs May is due to face a vote by Conservative chairmen on June 15 after resounding calls for her to quit. Pressure has since mounted against her as the Conservatives dropped to fourth place ahead of the European Parliament elections on May 23.
Mrs May has also been demanded to set a deadline for her cross party Brexit deal with Labour.
A senior minister told The Sun: “Such a head of steam is now building to just get anyone in instead of her now that it’s close to becoming inevitable.
“If she can’t find a majority for Brexit in the next couple of weeks, does she really risk abject humiliation at the national convention on June 15?
“Or does Philip sit down with a whisky and tell her it’s time.
“I suspect he’ll tell her not to put herself through that, and knowing her, she won’t want to put the party through that either.”
Negotiations between Mrs May and Jeremy Corbyn have reached their seventh week.
But Cabinet ministers have reportedly given up hope of a deal being struck ahead of the EU elections next week, according to the paper.
A senior Tory added Mrs May needs to set a deadline in order to stop them continuing for weeks, according to The Sun.
They added longer talks will inflict more damage on the Conservative party.
Mrs May’s departure could come sooner however as members of the 1922 committee have said Thursday is her “D-day”.
ITV’s political correspondent, Daniel Hewitt, wrote on Twitter: “Members of the Tory 1922 executive tell me Thursday is D-Day for Theresa May – they’ll demand a departure date when she addresses them, and if she doesn’t, they will vote on a change to party rules.
“This is her last chance’ one tells me.
“If we detect any messing about or equivocation, that’s it. She’s gone.”