The Sheffield city region mayor said he wanted to “play my part” in Labour’s future and refused to rule out running for the leadership – but said he would be “suspicious” of anyone announcing a bid at Christmas.
In an attack on Mr Corbyn’s record, he said the party had failed to offer a credible leader or programme for government and called for a “clean break with the past”.
Mr Jarvis also said the Labour leader’s senior aides such as Seumas Milne and Karie Murphy needed to quit amid an outcry over possible redundancies among junior party staff.
The former army officer would enter a crowded field, with Emily Thornberry and Clive Lewis having already announced their intentions to run. Keir Starmer, Lisa Nandy, Jess Phillips and David Lammy may also join the race.
The left of the party is thought to be coalescing around Rebecca Long Bailey, the shadow business secretary, who has kept quiet since Labour’s disastrous election showing.
Mr Jarvis, the MP for Barnsley Central, said traditional Labour voters in places such as South Yorkshire felt the party no longer represented them.
“Too many people said they weren’t prepared to vote Labour this time. We have got to listen to those people,” he told BBC Radio 4’s The World at One.
“Yes, it is about the leader. It is about having someone who you can credibly present to the country as a prime minister. You have to be credible when it comes to the economy and when it comes to national security.
“You have to have a manifesto programme that is credible and speaks of the challenges the country faces now and in the future. Those are the things that we didn’t do in the most recent general election.”
He added: “I think we need a clean break. We need a new leadership team, a new leader, new people coming into the shadow cabinet, some new advisers in the leader’s office: a clean break with the past and a fresh start.”
Mr Jarvis said he was not considering a tilt for the top job at present but then repeatedly failed to rule it out during a radio interview.
Asked whether he could rule it out, he said: “I will be slightly suspicious of anybody who is declaring their candidacy, certainly on Christmas Eve.
“I have a very, very significant commitment as mayor. I take that very seriously, but I do want to play my part. I care deeply about the Labour Party, care deeply about the country.
“Things have not gone well for us in recent times and we have a responsibility to reflect on that.”
Mr Corbyn is expected to stand down in the new year, with a new leader expected to be announced in March.
An exclusive poll for The Independent revealed voters want a decisive break from Mr Corbyn’s agenda, casting doubt over his claims to have “won the argument” in the aftermath of the election.
The BMG poll found that 46 per cent of voters think Labour should ditch its current agenda on tax and change course, while just 27 per cent are in favour of a policy similar to Mr Corbyn’s.