Tory grandee Ken Clarke has said he is willing to lead a government of national unity to avoid a no-deal Brexit.
Mr Clarke said it was "not inconceivable" that a government of national unity may be needed to resolve the impasse, suggesting politics was in a similar situation to 1931 and the two world wars.
He told BBC Radio 4's PM programme: "If it was the only way in which the plain majority in the House of Commons that is opposed to a no-deal exit could find a way forward... I wouldn't object to it, if that was the judgment of people, the only way forward.
"But there's an awful lot to be gone through before then and I haven't been taking part in any talks with anybody for the last fortnight.
"I've been on the phone to one or two people in the last couple of days just to find out what the devil's going on."
Ms Swinson is coming under increasing pressure to back Mr Corbyn’s suggestion, which includes forcing out Boris Johnson in a vote of no confidence and securing an extension to the Brexit deadline beyond October 31.
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But she has maintained her stance that he is not the right politician for the job, despite agreeing to meet with him to discuss a no-deal prevention plan.
On Friday, Mr Corbyn rejected her suggestion Tory grandee Ken Clarke or senior Labour MP Harriet Harman could lead the emergency government.
Mr Corbyn told PA: "It’s not up to Jo Swinson to choose candidates, it’s not up to Jo Swinson to decide who the next prime minister is going to be.
"Surely she must recognise she is a leader of one of the opposition parties who are apparently opposed to this Government, and apparently prepared to support a motion of no confidence."
Mr Corbyn said Ms Swinson should respect the "normal precedent" to allow the leader of the Opposition to form an administration after a successful vote of no confidence in the Government.
He also told politicians who were "making noise in the media" to consider supporting him in order to prevent a "damaging" no-deal Brexit.
Ms Swinson said she has spoken to her favoured candidates - the Father and Mother of the House - and won their assurances that they are ready to “put public duty first” to “stop us driving off that cliff”.
However, Mr Corbyn’s plan has won the potential backing of the SNP, Plaid Cymru and Tory MP Guto Bebb.
SNP leader Nicola Sturgeon was among those applying pressure to Ms Swinson to re-think her position.
Mr Corbyn announced his plan in a letter on Wednesday to opposition leaders and Tory MPs Dominic Grieve, Sir Oliver Letwin and Dame Caroline.
Remain-backing Tory MP Dominic Grieve appeared to agree with Lib Dem leader Swinson, saying "a government of national unity doesn't have to have a leader of any political party as its head".
However the former attorney general did say he and colleagues were "entirely serious" about talking to Mr Corbyn.
He told ITV News: "If we wants to talk to us about stopping a no-deal Brexit, I'm perfectly prepared to speak to him, as are my colleagues."
Although he added: "Putting in a caretaker prime minister must be for some useful purpose. My impression from the letter he's written to me is that he wishes to be a caretaker prime minister to trigger an election."
However, Nigel Evans, a member of the 1922 Committee of Conservative backbench MPs, told the BBC Radio: "We've filled the vacancy with Boris Johnson and so I really don't know what Ken is talking about."
Mr Evans added: "It does seem to be Westminster meets La La Land because it's not as if these ideas are half-baked, I really don't think they've been anywhere near an oven."