Pressure is mounting on John Prescott as his position as deputy prime minister is called into question by Labour politicians.
John Prescott: Lost department in reshuffle
Labour peer Baroness Kennedy told the BBC it was "timely" for Mr Prescott to leave his post.
Former minister Denis MacShane said the party needed renewing from bottom to top and that no-one's job was safe.
But a report in the Sunday Times of an organised plot to unseat Mr Prescott has been dismissed by backbenchers.
The paper said MPs were angry he had managed to keep his grace-and-favour homes despite losing his department.
It was among several Sunday papers to carry stories and snatched pictures of Mr Prescott, who is currently standing in for Tony Blair while the prime minister is on holiday.
It was further reported in the Independent on Sunday that Harriet Harman, Alan Johnson and Tessa Jowell were all interested in taking his job.
Ms Harman told GMTV she believed it was a "necessity" for the next deputy prime minister to be a woman.
"I think that we have to have a team of men and women in the leadership looking to men and women who after all regard themselves as equals now," she said.
According to the Sunday Times, documents being circulated among Labour MPs quoted former minister Angela Eagle as saying she "wouldn't rule out a signature collection" to force Mr Prescott out.
The paper said Ms Eagle had canvassed on behalf of Ms Harman as the next Labour deputy and believed female MPs and voters were "furious" with Mr Prescott over his affair with his former diary secretary Tracey Temple.
But Ms Eagle told the Press Association there was "no truth whatsoever" in the paper's allegation.
"I have seen no 'document'. I am not aware that any exist," she said.
"I have not spoken to the Sunday Times, much less given them any quotes."
Speaking on the BBC's Sunday AM programme, Baroness Kennedy said there was a feeling of "serious disappointment" that the events and coverage would undermine anything Mr Prescott now said.
"Every time he stands up to speak, people are going to be ribaldly making references to the photos we all know and we saw in the papers.
"There is an undermining of any kind of status that he might have within the party and I think people feel that a move on might be timely."
Former Labour minister Denis MacShane said he was "not happy" with the way the Prescott affair was handled and called for a "renewal" of the Labour Party.
"We are having an open debate. We need to renew our Labour Party from the very top to the very bottom and nobody's job, nobody's policy is protected," he told Sky News's Sunday Live.
However, as far as he was aware there was no plot to get rid of Mr Prescott, he added.
Mr Prescott won staunch backing from health minister Andy Burnham, who told the same programme: "I feel very strongly that John Prescott has done an excellent job for this government and he has been an excellent deputy prime minister. He has my full support in the job."
Photos published in the Mail on Sunday purport to show Mr Prescott playing croquet on the lawn of his country retreat Dorneywood, Buckinghamshire, just as he took over running the country when Mr Blair went on holiday.
Sir Christopher Meyer told Sunday AM the PCC's press code of conduct forbade the publication of photos taken with long-lens cameras on private property, unless there was a public interest in them being printed.
John Prescott was stripped of his department in Mr Blair's May reshuffle and now chairs nine Cabinet committees and deputises for Mr Blair when he is away.
The Conservatives have attacked Mr Prescott for keeping his salary and perks despite "seemingly doing very little".