Andy Burnham may have a new route to parliament after the MP Andrew Gwynne reached a settlement with the Commons that would allow him to retire and call a byelection.

The mayor of Greater Manchester is said to be seeking a return to parliament to stand for the Labour leadership if there is a challenge to Keir Starmer, but was thought to have limited options for a byelection in the north-west.

Gwynne, the MP for Gorton and Denton in Greater Manchester, has expressly denied planning early retirement. He was reported to have been seeking the settlement with the Commons pensions authorities but to have withdrawn the request in the autumn. Shortly afterwards, he said he planned to serve the full parliament.

But a senior source confirmed the MP, who is currently suspended from the Labour party, had now reached an agreement on his MP’s pension that would allow him to retire on medical grounds.

Gwynne is still subject to a parliamentary standards investigation, which was initiated last year after he was found to have been in a WhatsApp group that shared vulgar and inflammatory comments about voters and other MPs. He was suspended from the party after the messages came to light.

He was said by some MPs to have reached an agreement with Burnham to allow him to run in his seat after his early retirement, but Gwynne denied there had been any pact.

Burnham would have no guarantee of the nomination should he decide to try to return to Westminster in a byelection, which would be decided by a panel of members from the party’s ruling national executive committee (NEC).

The body is dominated by Starmer loyalists but there would be significant disquiet among MPs should members try to block Burnham. It is possible the body could impose an all-female shortlist in order to stop his nomination. A byelection for the mayor of Greater Manchester would also represent a multimillion-pound cost for the party.

Any byelection in the seat is likely to see Reform UK mount a significant challenge. Gwynne has an 18,000 majority in the seat, which lies to the south east of Manchester.

Should Burnham return to parliament, he would have to secure the backing of 80 Labour MPs to challenge Starmer.

Gwynne’s office has been approached for comment.