Greater Manchester Mayor Andy Burnham told Labour MPs by phone on Tuesday that he still intended to seek an imminent return to parliament, after two seats his backers had considered certain to secure as recently as Monday night fell out of contention. Burnham assured colleagues that he had options to return to the Commons and urged them to hold the line.

The two MPs concerned got cold feet, leaving Burnham's camp without a clear route back to Westminster. Several other sitting MPs whose constituencies have been floated as possible openings publicly ruled out making way.

Jeff Smith, who represents Manchester Withington, told the Press Association that he was not stepping aside for Burnham. Afzal Khan, the MP for Manchester Rusholme, also told the Press Association, "I am not." Khan added, "Voters had chosen him to represent them and that is the job I am focused on doing."

"I don't know how many different ways I can say this, but I'm not stepping aside for Andy Burnham," said Charlotte Nichols, the MP for Warrington North. Nichols said it was tedious for her and demoralising for her staff to keep seeing it reported that she might be about to go when there had never been a conversation with Andy about doing so.

Jim McMahon, who represents Oldham West and is known to be close to Angela Rayner, did not respond to inquiries about his parliamentary seat. Some in Burnham's camp have reservations about the Oldham West seat because they expect a well-funded Reform campaign there focusing on the town's legacy of grooming gangs. Marie Rimmer's seat of St Helens South and Whiston has also featured in speculation.

"We thought the local election results would concentrate some people's minds, but until you've got something lined up, you haven't," a Burnham ally said. "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."

Burnham has also held conversations with union leaders. A member of Labour's national executive committee said that, to win over some union support, Burnham 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. The last time he attempted to run, Burnham had been very far from having a majority on the national executive committee.