Theresa May is expected to meet the chairman of the powerful 1922 Committee of Tory backbenchers as pressure for her to set a firm departure date intensifies.
It is understood that the Prime Minister will have discussions with Sir Graham Brady in the wake of the committee requesting "clarity" on Mrs May's timetable for standing down and triggering a leadership contest.
With negotiations between the Government and Labour on trying to end the Brexit impasse set to continue on Tuesday, Tory impatience with Mrs May's failure to name a clear resignation date is increasing.
Mrs May has said she will step down if her Withdrawal Agreement is ratified, but has not made clear how long she intends to stay if no deal is reached.
The deadline for Brexit has been extended to the end of October.
Sir Geoffrey Clifton-Brown, treasurer of the 1922 Committee, put the spotlight on a departure date by insisting Mrs May announce a "road map" for her resignation after the European elections set for May 23.
He told the BBC: "We are now having to face the prospect of European elections which none of us wanted to face. They are going to happen.
"And, I would have thought that fairly soon after that would be time for her to think about setting a schedule to find her successor.
"That is regardless of whether there is a deal on offer or not.
"We should move on as Conservatives."
Reports that Mrs May is poised to propose a temporary customs arrangement with the EU as part of the talks with Labour also drew criticism from Sir Geoffrey.
He said: "It is unlikely that I will vote for a deal containing a customs union."
Shadow chancellor John McDonnell accused the Prime Minister of jeopardising the talks, claiming she had "blown the confidentiality" of the discussions.
He said he no longer trusts Mrs May, following the reports that she was prepared to give ground in three areas: customs, goods alignment and workers' rights.
Referring to talks with Labour, Children's Minister Nadhim Zahawi said: "Currently, if you look at the Withdrawal Agreement, the customs arrangements, or the alignment with the EU would go on until December 2021, if Labour believe, actually, that they would rather go to the next general election, which is 2022, for example, then, actually, that's still a temporary customs arrangement.
"And then, whoever is leader of the Conservative Party can then lay out their stall as to the next instalment of negotiations."
Mr Zahawi said a new referendum with Remain as an option would be bad for the country and seen as an attempt to "unpick" the result of the 2016 poll.
Labour MP Caroline Flint said Labour should push for a Brexit deal with the Tories.
Ms Flint told the BBC: "I think if a deal is struck in which Labour achieves many of its goals in that deal, that it takes us up to a general election in which all parties will be able to then set out their stall, then I think that is a deal that is worth pursuing.
"And if Labour signs up to a deal that includes those goals I think a majority of Labour MPs will support that position."
Reporting by PA
