The former chancellor gave his support to a proposal by Liberal Democrat leader Jo Swinson for an emergency government led by him or Labour's Harriet Harman.
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.
Mr Clarke continued: "A government of national unity is just one of the things that might be called for - it's not inconceivable - I mean we're in a similar situation to 1931 and rather wildly to the two world wars when the same thing happened.
"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's proposal came after she rejected Labour leader Jeremy Corbyn's suggestion he could lead an emergency government to thwart a no-deal Brexit, despite agreeing to meet with him to discuss a no-deal prevention plan.
He suggested it would seek an extension to Britain's EU membership and put together a "mandate for discussions that the majority of the House of Commons approved of, and a mandate that the Europeans would not resist".
"Then, once it had got that under way and set, it would call an election probably or resign and let's see if Parliament could form a party government of any kind that took it all forward and started resuming other politics," he said.
But he said Mr Corbyn would have to stand aside and let somebody else lead it because that is the "only way to get a multi-party group to come together".
Nigel Evans, a member of the 1922 Committee of Conservative backbench MPs, told the same programme: "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."
Today Mr Corbyn rejected Ms Swinson's suggestion that Mr Clarke or Ms Harman could lead the emergency government.
Mr Corbyn said: "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.
Anna Soubry, leader of the Independent Group, confirmed that she would also "not support nor facilitate any government led by Jeremy Corbyn".
"He cannot command unity of support amongst his own MPs, but now Jeremy Corbyn calls on the rest of us to back him as 'unity' Prime Minister," she said.
"And we won't even get a People's Vote, but instead a general election which as we know will solve nothing."
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.
Senior Remain-supporting Tories Dominic Grieve and Sir Oliver Letwin, as well as independent MP Nick Boles, have also agreed to meet Mr Corbyn.
But Mr Grieve today signalled he would not be backing the Labour plan, instead saying he was open to working with like-minded MPs to prevent a "catastrophic" no-deal.