Theresa May is expected to announce the date of her departure from Downing Street on Friday morning, senior cabinet ministers have told the BBC.
Sources say they expect the PM to give a timetable for her successor to be chosen, with 10 June likely to be the start of the official leadership race.
Mrs May is due to meet the chairman of Tory backbenchers on Friday.
She has been under pressure to resign, after a backlash by her own MPs against her latest Brexit plan.
Since January, Parliament has rejected the withdrawal agreement Mrs May negotiated with the EU three times. Recent attempts to find a formal compromise with Labour also failed.
legislation required to bring the agreement into UK law - describing it as "one last chance" to deliver Brexit.
However, her proposals - including a customs union arrangement and an offer to give MPs a vote on holding another referendum - angered many Tories.
Labour said it was a "rehash" and they would not support the plans.
Andrea Leadsom quit as Commons leader on Wednesday evening saying she no longer believed the government's approach would "deliver on the referendum result".
And on Thursday, Mrs May met Home Secretary Sajid Javid and Foreign Secretary Jeremy Hunt at Downing Street, where they are understood to have expressed their concerns about the bill.
BBC political editor Laura Kuenssberg says several cabinet ministers have said they expect Mrs May to announce her departure on Friday morning, although there has been no confirmation from Downing Street.
Ministers hope the campaign for the next Conservative Party leader can be finished by the end of July.
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Source: BBC
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