Sheffield City Region mayor Dan Jarvis has indicated he may join the race to replace Jeremy Corbyn as Labour leader.
Mr Jarvis, who is also MP for Barnsley Central, said he wants to "play my part" in the party's future.
He said he took his mayoral role "very seriously" and hinted he would reflect over the Christmas break on whether to run for the leadership.
Emily Thornberry and Clive Lewis have both officially entered the leadership contest.
Mr Corbyn will stand down "early next year" after Labour's election defeat.
Sir Keir Starmer, Yvette Cooper and Lisa Nandy have also said they were considering standing to be leader.
Speaking on BBC Radio 4's The World at One, Mr Jarvis says he has "a very, very significant commitment as mayor" but voters in the party's traditional heartlands like South Yorkshire felt Labour no longer spoke for them.
"Too many people said they weren't prepared to vote Labour this time. We have got to listen to those people," he said.
"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."
Asked about whether he would throw his hat in the leadership ring, he said: "I will be slightly suspicious of anybody who is declaring their candidacy on Christmas Eve."
Mr Jarvis was elected as Sheffield City Region's first mayor in May 2018.