Former Leeds City Council leader Jon Trickett who is MP for Hemsworth and a previous shadow cabinet member under Jeremy Corbyn, told journalist Owen Jones that Sir Keir Starmer had failed to deliver on promises made when he was elected in April last year.
It comes amidst mounting party divisions as Sir Keir is expected to announce a reshuffle of the shadow cabinet today (Sunday), following news that Deputy Leader Angela Rayner was removed from her positions as chair and national campaign co-ordinator.
Appearing on a live discussion hosted by Guardian columnist Jones, the MP said: "If it comes to the question if the leadership challenge, I don't think we should rule it out."
He added: "I want to hear what [Starmer] says, and I want to hear what the Party membership says. But I think we should be prepared for further developments."
Mr Trickett criticised Sir Keir's "refusal" to call for the resignations of Health Secretary Matt Hancock, Education Secretary Gavin Williamson and Dominic Cummings over the past year, instead saying he was too busy "looking behind" sacking members of his own party.
"I do believe in leadership," he continued, "but I also believe in listening to the people who you want to lead."
Jon Trickett backed Rebecca Long-Bailey in the 2020 Labour leadership contest, and was asked to stand down from the front bench following her opponent's victory.
Labour's poor results in council elections - notably among so-called "red wall" areas - and defeat to the Conservatives in the Hartlepool by-election have been described as "shattering" by shadow housing secretary Steve Reed, although the Party has had successes in regional mayor elections and in Wales.