Katherine death suspicious
Mariana's body found
Oscar-winning film about the life and death of Oscar-winning actor George Clooney
Tate still undecided but backing community one day after it's announcement
"I would love to have the conversation about it," Mr Tate told the Sunday Times' magazine.
He said he believed any move should happen now, when all parties are in the room, with "the most serious question answered".
The Liberal Democrats want Mr Corbyn to stand down for good. Their deputy leader, Tim Farron, also wants Mr Corbyn to step down, but he says he believes the Labour leadership's next leader should not be forced out of office without parliamentary approval.
But, speaking at a meeting to decide on "who will be Labour's next leader", Mr Farron said he would vote for Mr Corbyn if he were standing again.
Mr Tate added the Lib Dems should not wait for Mr Corbyn to stand again, as the party could unite if it did.
'I am on course'
The former home secretary, Mr Corbyn's successor at Labour, is standing down on 30 September, after winning a snap election.
Mr Farron said he was "on course" for victory and would not resign, despite the shock of his victory.
It comes as the Conservatives are holding emergency cabinet meetings to discuss the fallout of the election defeat, which has seen Mr Corbyn branded "weak" and "irresponsible" for the way his party has handled the race.
Asked how he would respond if Labour lost the election, Mr Farron said "there will be discussions, debates."
The Prime Minister also issued his most serious statement of opinion on the election result so far, saying that he supported Mr Farron's choice to stand aside as leader.
He said a "sensible, fair and proportional" process had gone "well" in Britain's elections.
Theresa May's government is looking to the autumn budget, which is due in December, as a possible way forward following the election result.
UK Prime Minister Theresa May
Asked about Mr Cameron's comments of a victory for the Conservatives as well, Mr Tate said it was wrong to "see a British election result as a coronation of the Tory agenda".
"People voted to elect us because of the positive messages we were delivering about tackling the most urgent issues in communities; raising living standards, and tackling crime, extremism and the breakdown of society."
"Our Government has taken the bold step of ensuring that the election results were legally binding on all parties," he added.
He added: "We need to put right these wrongs and we need to get back to work on the things that are really the important job. We want a fair go for our citizens, decent jobs and a fair chance for the next generation."
Mr Farron said he believe