Theresa May is due to meet senior Conservative MPs who are demanding she sets a date for her departure from Downing Street.
Under pressure from her MPs to stand aside, the prime minister is meeting the executive of the backbench 1922 Committee to discuss her future.
But current leadership rules mean she cannot be formally challenged until December.
Mrs May has said her departure depends on delivering Brexit.
Last month, the 1922 Committee executive narrowly decided against changing the party’s leadership rules to allow an early challenge to Mrs May.
But she was asked to provide a “clear roadmap” for her departure.
On Thursday, senior Conservative MPs are expected to press her to set out that timetable, regardless of whether Parliament backs her Brexit withdrawal agreement next month.
After the talks with the prime minister, the executive will hold another meeting where changes to the leadership rules could be discussed again.
Theresa May’s very long goodbye
Twice my colleague in Paris asked the prime minister if she would resign if her Brexit plan is rejected by MPs again. Twice she completely swerved the question.
You can’t blame her for wanting to avoid it. Theresa May is not exactly fond of revealing much in interviews in any case.
And for her to go anywhere near tangling with her potential exit would have breathed even more fire into the frenzied speculation.
But it is notable that the prime minister didn’t even repeat any of her rehearsed lines about her promise to see this phase of Brexit through, and then go.
Sir Geoffrey Clifton-Brown, treasurer of the 1922 Committee, said: “What I would like to see is her set out a timetable to trigger a leadership contest.”
He said it would be “infinitely preferable if she set a date rather than us force her out”.
Prominent Brexiteer Mark Francois said a predicted poor performance by the Conservatives in next week’s European Parliament elections would increase the pressure on Mrs May to stand down.
“As the polls increasingly suggest, we are going to have an extremely difficult night in the European elections,” the MP said.
When the results are announced, “my colleagues will finally wake up and smell the coffee if they have not, indeed, done so already,” he added.
The meeting between the 1922 Committee and Mrs May comes after she announced that the withdrawal bill, a collection of new laws needed to take us out of the EU, would be put to a vote in the Commons in early June.
Mrs May said the bill would “ensure that we deliver Brexit for the public”, while Brexit Secretary Stephen Barclay said the prime minister’s deal would be “dead” if MPs did not pass it.