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 time has come’
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.
Both the main parties suffered disappointing results in last week’s local elections – with the Conservatives losing 1,334 councillors and Labour failing to make expected gains, instead losing 82 seats.
The prime minister has blamed the Brexit impasse for the losses and has called on both sides to compromise to agree a deal.
However, tensions remain as talks between the government and Labour resume.
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.
However, BBC political correspondent Iain Watson said Labour sources had suggested they would not accept this.
The party 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 also said they would not vote for a customs union.