Theresa May has vowed to set a timetable for the election of her successor after the next Brexit vote in the first week of June.
The arrangement follows a meeting between the prime minister and senior Tory MPs who are demanding a date for her exit from Downing Street.
If she fails the vote on her Brexit plan, already forbidden three times, sources say she would quit.
Meanwhile, Boris Johnson has said he will run for lead once Mrs. May quits.
The prime minister lasted a confidence vote by Conservative MPs at the end of last year and party rules mean she cannot officially be challenged again until December.
But Mrs. May has come under growing pressure to leave Downing Street this summer, amongst the Brexit deadlock and poor results for the Conservatives in the recent local elections in England.