Tory Brexiteers are increasingly confident they have enough support to trigger a no-confidence vote in Theresa May as party leader.
If 48 Conservative MPs submit letters to say they no longer support her, a leadership challenge will be launched.
There is no confirmation but sources, including a cabinet minister, have said they believe 48 letters have been sent.
The BBC has also been told the senior backbencher who receives the letters has asked to see the PM on Wednesday.
However Sir Graham Brady, who chairs the backbench 1922 committee, would make no comment.
Downing Street sources are playing down an imminent move and say they have had no contact from him.
The backbench challenge to Mrs May as Conservative leader has been led by those unhappy at the Brexit deal she negotiated, which they argue would keep the UK closely tied to the EU in the long term.
Some Tories who voted Remain in the referendum are unhappy too.
Separately, many opposition MPs have urged Labour leader Jeremy Corbyn to call for a Commons vote of no confidence in Mrs May as prime minister, though he has so far resisted.
Mrs May spent Tuesday meeting EU leaders and officials in The Hague, Berlin and Brussels, in efforts to salvage her deal, which is widely opposed by MPs of all parties, who voted both Leave and Remain in the EU referendum.
Her decision to delay the vote on the terms of the UK’s withdrawal from the EU, which had been due to take place on Tuesday, has caused anger across the Commons.