Andy Burnham "could be the answer" to Labour's ongoing problems, Geoff Hoon has told GB News.
Speaking to the People's Channel, the ex-Labour Defence Secretary said he is "fairly confident" that Mr Burnham will be confirmed as the by-election candidate in Makerfield.
Asked by host Ellie Costello if he believes Mr Burnham is the "right person to fix the party’s problems", Mr Hoon agreed.
He admitted: "Well, he might be. I think what's important is to see what happens, assuming that he is elected in Makerfield.
"There will then be, I'm sure, more speculation about a leadership challenge and so on. But I think it's important that we don't get ahead of ourselves."
Mr Hoon declared that Sir Keir Starmer and the Labour Government should "go on governing the country".
He told GB News: "We have a Prime Minister, we have a Government, and they rightly need to go on governing the country.
"That's their job day to day, and we need to allow them to do that job."
The former Labour Chief Whip dismissed suggestion by Ellie Costello that Wes Streeting is seeking to "sabotage" Mr Burnham with his stance on Europe.
He hit back: "I don't accept that for a moment, Wes Streeting has just resigned from the cabinet on a question of principle.
"He disagrees with the direction of Keir Starmer's Government and has chosen to resign from a very high-profile, important position.
"In those circumstances, what comes with resignation is the freedom to speak out, and it's hardly surprising that he chooses to set out his views at this stage after such a high-profile resignation."
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He also said that Sir Keir should not have to set out a timetable for stepping down telling GB News he "doesn't accept that".
He made clear: "The Prime Minister, less than two years ago, won an overwhelming mandate from the British people to Govern."
As host Alex Armstrong disagreed that the result was "overwhelming", Mr Hoon also suggested Britain's first-past-the-post system may no longer be fit for purpose.
He explained: "It was overwhelming in our parliamentary democratic system.
"We may have a discussion, perhaps on another occasion, about whether those arrangements currently fit the purpose of a society that has now a number of different political parties rather than simply two main ones.
"That's a debate for another day, but undoubtedly, in terms of our present rules, he won an overwhelming majority in the House of Commons."
No10 has dismissed speculation that Sir Keir is planning to step down, pointing to comments he made in an Observer interview eight days ago as still representing his position.
A No10 spokesman said: "There will be no timetable for departure. We are delivering for the British people and accelerating the pace of change. The PM is fully focused on it."
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