Andy Burnham has told Labour MPs they should hold the line and that he has options to return to parliament after several seats identified by his allies failed to materialise.

Two seats that backers of the Greater Manchester mayor had described as “nailed on” as recently as Monday night are now out of contention after the MPs concerned got cold feet.

Burnham spoke to a number of MPs by phone on Tuesday and assured them that he still intended to seek an imminent return to parliament.

The Guardian was told by two MPs on Wednesday that Jeff Smith, who represents Manchester Withington, an affluent suburb of the city, was in talks about stepping aside for Burnham, but his friends denied it. Smith was approached for comment.

Afzal Khan, the MP for Manchester Rusholme, has also denied his seat is in contention.

Jim McMahon, who represents Oldham West, did not respond to inquiries about his seat, but he is known to be close to the former deputy prime minister Angela Rayner, another possible contender for the Labour leadership. There are some in the Burnham camp who have deep reservations about the seat anyway because of the likelihood of a well-funded Reform campaign there, and especially a focus on the town’s dark legacy of grooming gangs.

Burnham’s allies had previously been confident they had potential seats for him in Warrington North and St Helens South and Whiston, but the MPs for these constituencies, Charlotte Nichols and Marie Rimmer, deny that was the case.

“I don’t know how many different ways I can say this, but I’m not stepping aside for Andy Burnham,” Nichols said on Wednesday. “It’s both very tedious for me and very demoralising for my staff to keep seeing it reported that I might be about to go when there’s never even been so much as a conversation with Andy about doing so.”

One Burnham ally said: “We thought the local election results would concentrate some people’s minds [but] until you’ve got something lined up, you haven’t. There’s been a couple of near misses but it’s difficult because it depends how colleagues feel [about their own political future]. We were hopeful something might come up and it hasn’t.”

Another MP, a key Burnham supporter, put it bluntly: “They’ve fucked it. Everything is falling apart, they’ve run out of time.”

A third pro-Burnham source said it looked as if any leadership race would move too fast for the mayor, with Wes Streeting expected to start an accelerated process this week. “It’s a big shit cocktail. We’re all doomed,” they said.

Burnham is understood to have had conversations with union leaders, but one member of Labour’s national executive committee (NEC) said that in order to win over some he would have to distance himself from elements of the energy policies promoted by Ed Miliband, because the GMB and others were pushing for a change in position.

They said Burnham had been very far from having a majority on the NEC the last time he attempted to run, but another source on the committee said that if Starmer’s political authority was shot Burnham would possibly have a chance. “Everyone on there is a pragmatist,” they said.

Burnham has been the preferred candidate for many MPs on the party’s soft left, including influential figures such as the former ministers Louise Haigh and Miatta Fahnbulleh, as well as more centrist MPs such as the former minister Josh Simons. But the group is likely to split significantly should Streeting launch a challenge and Burnham be unable to return in time.

Should Starmer decide to run against Streeting – and an alternative candidate from the left – the prime minister would have a major advantage because of Labour’s voting system, which is preferential.

MPs say they are deeply concerned that because Starmer would be likely to collect most second preferences, in a three-way contest he could even come second and still remain leader and prime minister.

Many told the Guardian they were split between backing Miliband or Rayner, or keeping Starmer in place to buy Burnham more time.

“Ed has got no hope with the unions, he has no path,” one senior MP said. “Lots of us might nominate him for want of anything and then sit it out. The Tribune group is split, massively.”

Another MP who backs Burnham said: “Andy’s best hope now is to do a deal with Keir – give him some time, let him build a legacy on Iran and Ukraine, finish the bills he cares about and have a transition that allows Andy to return. I think there are some in No 10 that are open to that, in theory, if the polls look as bad as they are. But they are worried, of course, about losing even more political authority if that comes out.”