Mr Corbyn, who is due to be replaced in April after announcing his departure following last year's general election, announced he would be happy remain in the frontline of British politics during a visit to flood-hit South Wales.
Leadership contender Rebecca Long-Bailey, the shadow business secretary, previously hinted she would offer Mr Corbyn a job if she becomes Labour's new leader.
Deputy leadership contender Richard Burgon also said he would like Mr Corbyn to be shadow foreign secretary.
"I am happy to serve the party in any capacity because my whole life has been about making my contribution in Parliament, holding governments to account and of course speaking out on policy areas," Mr Corbyn said during a visit to flood-hit South Wales.
"I have been proud to lead the party for the past five years, proud of the policy achievements we have made and of the huge growth in membership."
Asked to confirm that he would accept a position, if offered, Mr Corbyn replied: "See what it is.
"I didn't know I was going to be offered anything and you're telling me something that I didn't know."
If Mr Corbyn were to remain on Labour's frontbench he would become the first leader since Ramsay McDonald to do so.
The ballot in the leadership contest had been due to open on Friday.
However, it emerged voting was being delayed until Monday. Labour did not immediately explain why.