The Prime Minister may offer a "clear understanding" of her timetable for departure next week, the chairman of the backbench 1922 Committee has said.
Theresa May has previously suggested she will leave Downing Street after her Brexit deal has been passed by Parliament.
But Sir Graham Brady, chairman of the committee since May 2010, told BBC Radio 4's Week in Westminster that Mrs May had offered to meet with the executive following a request for "clarity" on her plans.
He told the programme: "It would be strange for that not to result in a clear understanding... at the end of the meeting."
The Altrincham and Sale West MP added he understood her "reticence" to set a date, but added: "I don't think it's about an intention for staying indefinitely as prime minister or leader of the Conservative Party.
"I think the reticence is the concern that by promising to go on a certain timetable, it might make it less likely she would secure Parliamentary approval for the withdrawal agreement, rather than more likely."
Earlier this week, Mrs May rebuffed demands to set out a timetable for her departure from No 10 amid growing pressure from Tory MPs to make way for a new leader.
At Prime Minister's Questions, Brexit-backing Andrea Jenkyns told Mrs May she had "failed" in EU withdrawal negotiations and forfeited the trust of the public.
"The public no longer trust her to run Brexit negotiations," she said.
"Isn't it time to step aside and let someone else lead our country, our party and the Brexit negotiations?"
Mrs May retorted: "This is not an issue about me and it's not an issue about her.
"If it were an issue about me and the way I vote, we would already have left the European Union."
Downing Street made clear the Prime Minister was not ready to go beyond her earlier promise to the 1922 to quit as Tory leader when the first phase of Brexit negotiations – dealing with the divorce terms – is complete.
"The PM made a very generous and bold offer to the 1922 Committee a few weeks ago that she would see through phase one of the Brexit process and she would leave and open up for new leadership for phase two," a No 10 source said.