Andy Burnham has said MPs have privately called on him to challenge Sir Keir Starmer to become prime minister.

In the Telegraph the Manchester mayor, who is not currently an MP, said he was not “plotting to get back” to Westminster but in the interview he did not rule out running again for the leadership.

“I stood twice to be leader of the Labour Party. And I think that tells you, doesn’t it?”

His latest interview comes ahead of Labour’s autumn conference, and after Sir Keir faced pressure from some MPs following the resignation of his deputy Angela Rayner and his sacking of Peter Mandelson.

The mayor also told the Telegraph that Number 10 had created a “climate of fear” among some MPs.

“People have contacted me throughout the summer”, he said when asked if other MPs had urged him to run for the Labour leadership.

“I’m not going to say to you that that hasn’t happened, but as I say, it’s more a decision for those people than it is for me.”

His comments, likely to be seen as a pitch for a leadership bid, come after his interview with the New Statesman on Wednesday where he criticised the prime minister’s approach, saying there needed to be “wholesale change” to see off an “existential” threat to Labour.

He said he was not attracted to going back to the old way of doing things in Westminster but added: ” I’m happy to play any role. I am ready to play any role in that. Yes. Because the threat we’re facing is increasingly an existential one.”

Burnham said he was ready to work with anybody with a “plan to turn the country around” – including the Liberal Democrats and Jeremy Corbyn.

Those around him say those comments have nothing to do with leadership ambitions, dismissing that as “Westminster speculation”.

But they also say that Burnham felt that something needed to be said about the “factional” way Number 10 was operating, as well as the need for the prime minister’s team to listen to a wider range of voices.

“What we need is a plan to defeat Reform,” one ally said.

A Labour source said: “I’ve heard of a stalking horse, but this guy is going to get hoarse from his endless stalking.”

In the later interview with the Telegraph he said higher council tax on expensive homes in London and the South East; £40bn of borrowing to build council houses; income tax cuts for lower earners; and a 50p rate for the highest-paid would “turn the country around”.

In previous leadership campaigns Burnham lost out to Ed Miliband in 2010 and Jeremy Corbyn in 2015.

Sir Keir has faced mounting pressure from within his party over his handling of the row over Peter Mandelson, who was eventually sacked as the UK’s ambassador to the US following more details emerging about his friendship with convicted paedophile Jeffrey Epstein.