Keir Starmer is understood to be discussing a plan to handover the Labour leadership to Andy Burnham in September amid a growing belief that he will announce his timetable for departure early this week.
The former Greater Manchester mayor is understood to want to wait to become prime minister until September and a delay would, according to a source, “allow the prime minister to secure his legacy.”
The source said that the prime minister is now “working towards” a handover.
But a deal would be dependent on Mr Burnham also securing a deal with Wes Streeting who has made it clear he wants to run for the leadership as well.
And a number of Labour MPs are concerned that a September handover will provide more delay and uncertainty.
One backbencher said: “Three more months of incapacitated government to go with the five months we’ve already had building up to this point. The Labour Party doesn’t understand the nature or realities of power.”
The revelation came after tech secretary Peter Kyle confirmed that Sir Keir is considering resigning as he spends the weekend “thinking through the political realities” of his situation.
With reports swirling that he is planning to announce a timetable for his departure as early as Monday, the prime minister is holed up in his country residence Chequers taking soundings from ministers, friends, allies and his wife Victoria.
However, foreign secretary Yvette Cooper has told the prime minister this weekend that he should go, it is understood, repeating her demands from last month.
It follows pressure mounting for Andy Burnham to replace Sir Keir in “a coronation” after the former mayor of Greater Manchester crushed Reform UK in the Makerfield by-election on Thursday.
Sir Keir only broke his silence over the weekend to put out a message on Fathers’ Day.
However, Mr Kyle confirmed that he had a long conversation with Sir Keir on Friday but refused to say what advice he gave amid speculation he is one of the cabinet members who told him he needs to set a timetable for his departure.
But confirming the prime minister is planning his departure, he added: “He is taking time to think through what the political realities are today compared to last week.”
Asked by the BBC’s Laura Kuenssberg if Sir Keir will resign Monday, he replied: “I can’t predict the future, I’m not his spokesperson, I’m not with him today.”
Downing Street has already denied the reports pointing to comments by Sir Keir on Friday that he would take part in a leadership contest.
Describing his conversation with Sir Keir, Mr Kyle said: “The prime minister was calm. He was thoughtful. He led the conversation. He was thinking about what is best for the country.”
However, transport secretary Heidi Alexander is understood to have told the prime minister his time is up on Friday while energy secretary Ed Miliband, Ms Cooper and home secretary Shabana Mahmood have also told him to set a timetable for his departure.
The Independent has already revealed that Sir Keir has been given a deadline of Tuesday morning’s cabinet meeting to make an announcement on his departure or “face humiliation” in a “brutal” leadership contest.
If he doesn’t announce a timetable to depart Downing Street, the prime minister is set to be hit with a wave of ministerial resignations.
But it is clear that when Mr Burnham does, as expected, become Labour leader and prime minister, there will be wholesale changes in his cabinet.
In a sign that he may not have a future as a cabinet minister in a Burnham government, the business secretary revealed that he had not received a reply to his text congratulating him on the Makerfield result.
Asked by Sir Trevor Phillips on Sky News if Mr Burnham replied to his congratulations, Mr Kyle said: “No, he didn’t. But it was yesterday, he’s very very busy.”
Mr Kyle is known to be an ally of former health secretary Wes Streeting who is also planning a leadership challenge but is now understood to be having discussions about doing a deal with Mr Burnham with the potential of becoming chancellor.
Former home office minister Jess Phillips has told Laura Kuenssberg that “this is it” for Sir Keir and said he needs to “resign with dignity.”
But fellow Labour MP Toby Perkins told the show that “there is no need for a contest” adding that “all the indicators are going the right way.”
Luke Charters, a Burnham ally, insisted that Makerfield was an important moment in political history and it is “right that the prime minister spends the weekend to reflect.”
More than 100 Labour MPs have already publicly told Sir Keir that his time is up as they look to bounce back in the polls against a wounded Reform UK and Nigel Farage.
But opposition parties are already looking to a Burnham government and what that would mean for the country and economy.
Tory shadow chancellor Sir Mel Stride has suggested that Andy Burnham as prime minister could spark chaos in the financial markets.
With speculation he could tear up spending rules under pressure from the trade unions after saying he wants to reverse 40 years of liberal “trickle down” economics, there are fears he will undo the stability created by chancellor Rachel Reeves.
Sir Mel said: “The markets are watching. And I think Andy Burnham taking over would be bad and in the wrong direction.” He added that Mr Burnham has “flip-flopped all over the place” during the by-election.
Meanwhile, two independent MPs are eyeing rejoining the Labour Party in parliament if Sir Keir goes.
Karl Turner was suspended over his vocal opposition to watering down the right to a jury trial while Rosie Duffield left the party after suffering abuse for standing up for women as well as anger over other policies.
Ms Duffield posted: “What exactly do you think we should be ‘grateful’ to Starmer for? This is our workplace, and both Karl and I can speak honestly about the nasty, technocratic, politically illiterate management that us/ our colleagues (now free to speak out too as they’re doing) have experienced.”