Deputy leader Tom Watson is the latest Labour figure to say a leadership contest is “inevitable” after Mr Corbyn refused to resign.
A source close to Mr Watson told the Press Association that he had tried to talk to Mr Corbyn about standing down but he refused to “engage”.
The deputy leader will not be a candidate in the contest, the source added.
“He tried to talk to him about going.
“He didn’t want to engage. He won’t stand himself but a leadership election is now inevitable,” the source said.
Former Labour leader and Doncaster North MP Ed Miliband called on successor Mr Corbyn to quit as Labour leader, saying his position is “untenable”.
The former party leader said he had supported Mr Corbyn “all the way along” but urged the Opposition leader to now reflect on what is “the right thing for the country”.
Britain is facing its worst crisis since the Second World War, Mr Miliband said.
He told BBC Radio 4’s The World At One programme: “I have reluctantly reached the conclusion that his position is untenable.”
Gordon Brown also joined the chorus of calls for a change of leadership.
He said: “The real issue comes down to whether we decide we are a party of power (or) a party of protest.
“And that means a party of power with principles that we wish to implement in practice.
“Either the Labour Party will become an anti-globalisation protest party, or it’s going to become a party that is able to tell people how we can best manage.”
Yesterday four unions Unite, the GMB, Unison and the CWU were in private talks over their response to the Labour Party deadlock and were planning to release a joint statement late last night.
Meanwhile Mr Corbyn attended a rally at the School of Oriental and African Studies (SOAS) in central London to speak to his young supporters.