Left-wing candidate Rebecca Long-Bailey has said she would offer Corbyn a role if she wins the race to succeed him, while deputy leader hopeful Richard Burgon said he would make him shadow foreign secretary.
If he took up a position, Corbyn would be the first Labour politician since the war to remain on the frontbenches after stepping down as leader.
Speaking during a visit to a flood-hit area of South Wales, Mr Corbyn appeared surprised to hear that Ms Long-Bailey was ready to offer him a post.
Asked if he would accept the job offer, Mr Corbyn said: “I’ll see what it is, I didn’t know I was going to be offered anything.”
He added: “I’m happy to serve the party in any capacity.
“My whole life has been about making my contribution in parliament, holding the government to account and for speaking up in policy areas.
“I have been proud to lead the party over the last five years, proud of the policy achievements we have made and the huge growth in membership.”
Ms Long-Bailey is reported to have told supporters in London earlier this month she would hand Mr Corbyn a high-level brief if she defeats Keir Starmer and Lisa Nandy to the top job on 4 April.
The Salford and Eccles MP said: “I’d like to but I don’t know whether he wants to do it because he said not… It’s up to him. I love him so.”
Mr Burgon has said Mr Corbyn could continue to play a “valuable role” on Labour’s front bench, saying: “If he was shadow foreign secretary, that would be ideal.”
Ms Long-Bailey, who has been publicly backed by John McDonnell and Jon Lansman, the founder of the pro-Corbyn Momentum group, has been fighting to shake off the “continuity Corbyn” label.
She said last weekend: “Jeremy and I are friends but it’s quite disrespectful when I’m termed the continuity candidate.
“I’ve always been strong in my principles, people know what I believe in.
“To suggest I’m a continuation of any individual is disrespectful, not least because I am a woman.”
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