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 the government, although he has so far resisted.
If such a vote succeeded, it would start the clock on a 14-day deadline to find a successor government which could command confidence. Otherwise, the Queen would have to dissolve Parliament.
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 voting 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.
What have Conservative backbenchers said?
So far, 27 Tory MPs have publicly stated they have sent letters saying they have lost confidence in their leader – but speculation has increased that the numbers have risen.
Former environment secretary Owen Paterson was among the latest to call for Mrs May to go, saying she had failed to prepare for a no-deal Brexit, tried to bounce her ministers into supporting her and approached negotiations like a “feeble and unworthy” supplicant.
“These mistakes have eroded trust in the government, to the point where I and many others can no longer take the prime minister at her word,” he wrote in his letter, published by the Daily Telegraph.
“She has repeatedly said ‘no deal is better than a bad deal’, but it is clear her objective was to secure a deal at any cost.”
But former cabinet minister Damian Green, who supports Mrs May, told BBC’s Newsnight: “If people have written letters to this degree… this is an act of monumental self-indulgence.
“People outside the Westminster bubble will be looking at this thinking ‘we have got a prime minister doing really difficult negotiations at the sharp end of one of the most important decisions this country has taken in 50 years’.
“To undermine a prime minister at this stage seems to me to be wholly wrong.”
What has Mrs May said?
Asked on Tuesday whether she had been told the threshold of 48 letters had been reached, Mrs May replied: “No, I have been here in Europe dealing with the issue I have promised Parliament I would be dealing with.”
She is due to travel to Dublin later after hosting a weekly meeting of her cabinet and facing Prime Minister’s Questions.
The PM is then scheduled to attend a summit of European leaders on Thursday at which she is likely to press for changes to elements of her Brexit deal to try to get the support of Parliament.
Speaking on Tuesday, she said there was a “shared determination” among EU leaders to solve the Irish border problem preventing MPs from backing her deal.
European leaders have said they will not renegotiate the text of the withdrawal deal agreed last month, as demanded by many Tory MPs, but are prepared to clarify aspects of it.
What are the rules for challenging the Tory leader?
It is not clear when a contest – if there is one – might take place, but Sir Graham has said in the past it would not be delayed unduly if the threshold were met.
The BBC’s Laura Kuenssberg said Monday was a possibility.
If a confidence vote is triggered, all 315 Tory MPs will be entitled to take part in a secret ballot in which they will be asked if they still have confidence in the prime minister.
If Mrs May wins the support of a majority of MPs – that is, 158 MPs – she would be entitled to carry on and, if she did, she could not be challenged for another year.
If a majority of MPs do not support her, she would have to resign as Tory leader and would also be expected to stand down as prime minister.
A leadership contest would then be held to succeed her which could take several weeks.
Some commentators have suggested that, given the weakness of her political position, it would be difficult for Mrs May to stay on if more than 100 MPs voted against her.
Analysis: It feels different this time
The BBC’s Laura Kuenssberg
I know, I know, I know. We have been here before, and on more than one occasion.
But senior Eurosceptics are more sure than ever that they have enough support to trigger a vote of no confidence in the prime minister. That doesn’t mean it is bound to happen.
The last time they said so, and said so pretty publicly, their confidence was a mirage and the numbers did not emerge.
It became evident to ardent Brexiteers that their communications between each other were not all genuine, and painfully so. Those who had told colleagues that they had submitted the letters, patently had not done so.
What feels different now is that those who take this all extremely seriously, who had their hopes dashed the last time, are suggesting privately – not necessarily with glee – that they might have done it this time, and crucially if the list isn’t long enough now, they have more MPs ready to join the calls.
Read Laura’s blog