The MP for Birmingham Yardley reportedly told the Cheltenham Literature Festival said Mr Corbyn should stand down if Labour isn’t the largest party in the next election.
According to The Times, she told the festival she would consider running to be his successor if she had a “genuine plan for the future of the country”.
Her comments come after shadow chancellor John McDonnell said he and Mr Corbyn would stand down if Labour loses the next election.
In an interview with former Labour spin doctor Alastair Campbell for GQ magazine, Mr McDonnell said he "can't see" how he or Mr Corbyn could continue to lead the party if they fail to win power after the next general election.
“What we'd do is as the tradition, which is have an election for a new leader,” he said.
Mr McDonnell said a woman should take over and named shadow education secretary Angela Rayner as a possible successor to Mr Corbyn.
"I'm still of the view now that whoever comes after Jeremy has got to be a woman," he said.
"We've got to have a woman leader. If you look at the new youngsters that have come through, they are fantastic."
But despite his comments, he said Labour could still "win a majority" in an election.
“I think we can win a majority, but if we go into a minority government situation, there will be no deals, we'll just lay out our programme and they either support it or they don't," said the Hayes and Harlington MP.
“If they don't support it we'll go back to the country and it will be interesting, if they did, to see how they argue against a real living wage, investment in public services, restoration of trade union rights, tackling climate change. How can they argue against that?”