The former health minister Andrew Gwynne has dismissed as “idle speculation” reports he could resign his seat as part of an Andy Burnham “coup” against Keir Starmer.

Allies of Burnham were reported on Sunday to have identified a shortlist of seats to allow the Greater Manchester mayor to return to Westminster in the new year.

One of these seats is said to be that of Gwynne, who was suspended by the Labour party in February after a leak of offensive WhatsApp messages.

One source was quoted as saying that Burnham allies had found a “nailed on” constituency, while another reportedly said a seat was “likely to come free shortly” before the local elections in May.

In a post on X on Sunday, Burnham dismissed the reports as “quite a lot of rubbish”, adding: “Reminds me why I left Westminster in the first place!”

However, the former health secretary – who has been critical of Starmer’s leadership – has repeatedly refused to deny he would return to parliament if the opportunity arose. A recent poll of Labour members suggested Burham would be the most popular candidate to replace Starmer.

Andy Burnham, pictured with Keir Starmer last year, dismissed the latest reports as ‘quite a lot of rubbish’. Photograph: WPA/Getty Images

Gwynne, 51, is undergoing treatment for serious health issues and has not returned to Westminster since he was sacked as health minister in relation to the WhatsApp messages, which he called “badly misjudged”.

Speaking publicly for the first time since his dismissal, he told the Guardian that he had no intention of standing down imminently.

“I can categorically say that no decision has been made on whether I stand down or fight the next general election – but I have no plans to stand down before the May elections,” said the MP for Gorton and Denton in Greater Manchester.

Gwynne said Burnham was a “close family friend” and that there had been “no conversations at all with him about me standing down”.

He added: “He’s a decent guy and he knows I am poorly and there’s been no pressure from him at all. Idle speculation like this does not help.”

Gwynne, a longtime Burnham ally who ran his mayoral campaign in 2016, remains under investigation by the parliamentary commissioner for standards.

Labour sources play down reports that the Great Manchester mayor was “on the brink of a major breakthrough” in returning to Westminster.

They pointed out that the mayor faced several hurdles before he could fight any byelection, not least being allowed by Labour’s ruling national executive committee to run as a candidate.

Some suggest Starmer would seek to block Burnham from standing for election and potentially mounting a leadership challenge, although others said this tactic would make the prime minister look weak.

With Labour trailing Nigel Farage’s Reform UK in the polls by an average of 9 percentage points, party sources said virtually no seat was a guaranteed path to victory for Burnham.

Gwynne, who won the seat with a 13,000-vote majority last year, is facing a challenge from Reform and the Green party as Labour loses votes nationally to the left and right of politics.

Labour figures have previously told the Guardian that Burnham could arrange a “job swap” with Jim McMahon, the MP for Oldham West, Chadderton and Royton, who lost his ministerial job in the reshuffle in September.

The demotion is said to have frustrated McMahon, who allies said fancied Burnham’s job as Greater Manchester mayor. However, pollsindicate McMahon’s seat would be lost to Reform and that Labour faces losing other previously-loyal voters in the constituency to pro-Palestinian independents.

Shabana Mahmood, the home secretary, said everyone in Labour had a “role to play” in supporting the government when asked about the latest Burnham speculation.

Speaking on Sky News on Sunday, she said: “Wherever you sit in the Labour family, we all have a role to play in supporting the Labour government deliver for the people of this country.”

Burnham and McMahon have been approached for comment.