Theresa May is to meet the chairman of an influential committee of backbench Tory MPs, Sir Graham Brady, amid calls for her to set a firm resignation date.
No 10 insists the meeting is routine but BBC political correspondent Iain Watson said Sir Graham is likely to press the prime minister for a timetable for her departure.
Meanwhile, cross-party talks to break the Brexit deadlock are due to resume.
In March, Mrs May pledged to stand down if and when Parliament ratified her Brexit withdrawal agreement with the EU – but she has not made it clear how long she intends to stay if no deal is reached.
The UK had been due to leave the EU on 29 March, but the deadline was pushed back to 31 October after Parliament was unable to agree a way forward.
The meeting comes amid growing pressure on Mrs May to step down as leader.
On Monday, Sir Geoffrey Clifton-Brown, treasurer of the 1922 committee – an elected body of MPs which represents backbenchers and also oversees leadership contests – told the BBC that Mrs May should announce a “road map” for her resignation after the European elections set for 23 May.
Leading Eurosceptic Sir Bill Cash also told the Press Association “the time has come” for her to resign.
“She needs to be given a date. The sooner the better. But it needs to be done in an orderly manner,” he said.
But Education Secretary Damian Hinds said people should not “read too much” into the timing of the PM’s meeting with Sir Graham.
“The prime minister has already been clear and straightforward that she will see through this first phase of Brexit,” he told BBC Breakfast.
And senior Tory backbencher Sir Oliver Letwin said he believed the PM would remain “in situ” until any Brexit agreement was finally approved by MPs.
Mrs May, who will chair a cabinet meeting later, survived a vote of confidence of her MPs at the end of last year. Under party rules, another vote cannot be held until December 2019.
But local Conservative associations are pushing for a vote of confidence in her next month which, although it would not be binding, would increase the pressure on the PM after last week’s local election drubbing.
The Conservatives lost 1,334 councillors in England, a performance which Mrs May blamed on the Brexit impasse.
The prime minister has urged Labour, which failed to make expected gains in the polls and instead lost 82 seats, to compromise to agree a deal.
However, tensions remain as talks between the government and Labour resume.
‘Lack of trust’
Labour’s shadow chancellor John McDonnell has said he does not trust the prime minister – after details from cross-party talks were leaked to the press – and accused her of having “blown the confidentiality” of the talks.
Reports emerged at the weekend that the prime minister was ready to offer a temporary customs arrangement with the EU that would last until the next general election.
Labour has previously said it wants a permanent customs union – an arrangement not to carry out checks or put tariffs (extra payments) on goods that move around an area.
A number of senior Tory Brexiteers have said they would not vote for a customs union, while two-thirds of Labour MPs say they will not back any agreement without a public vote.
The BBC’s political editor Laura Kuenssberg said this meant the leadership of both parties would be wary of signing up to anything likely to “implode” when it reached Parliament.
Labour MP Mary Creagh said the PM’s authority had been fatally damaged and suggested her party “needs to be wary of the embrace of a drowning woman”.
She urged Jeremy Corbyn to recognise the results of last week’s elections and “listen” to Labour members, who she said were overwhelmingly in favour of another referendum.
“The leadership will not get this through without a public vote attached,” she BBC Radio 4’s Today. “If we stand in the middle road on Brexit we get run over from both directions.”