Ms Swinson said the pair are ready sabotage the Brexit process to “stop us driving off that cliff”. It comes after Labour leader Jeremy Corbyn called on opposition parties and Tory rebel MPs to make him caretaker prime minister to avoid a no deal Brexit under Boris Johnson.
Mr Corbyn put forward his plan to oust Mr Johnson with a no-confidence vote, extend the Brexit deadline beyond October 31 and hold a snap general election.
The SNP, Plaid Cymru and Tory MP Guto Bebb have all suggested they could back the left-winger’s plot.
Pro-Remain Tory rebels Dominic Grieve and Sir Oliver Letwin, as well as independent MP Nick Boles, have also agreed to meet Mr Corbyn.
But the Lib Dems have refused to support the Labour leader, branding his proposal “nonsense”.
Ms Swinson has instead put forward Mr Clarke and Ms Harman, who are Father and Mother of the House, to lead the coalition of Remainers.
The Lib Dem leader told BBC Radio 4’s Today programme: “I have been in touch with them because obviously you don’t just mention people’s names without checking that they’re okay with that.
“They put public duty first, and they don’t want to see a no deal Brexit, and if the House of Commons asks them to lead an emergency Government to get our country out of this Brexit mess and to stop us driving off that cliff to a no deal, then yes, they are prepared to do that and I think that is to their credit.”
Energy minister Kwasi Kwarteng hit out at claims Mr Clarke could the country to disrupt Britain’s planned exit from the EU on October 31.
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“All of this seems to me like speculation about Ken Clarke and Harriet Harman and all these people. I don’t see them leading a Government.
“I think we have a Prime Minister and we’ll deliver on the mandate and the referendum of 2016.”
And Mr Corbyn has blasted Ms Swinson for rejecting his plan.
He 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 added 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.
The Lib Dem leader is facing increasing pressure to sign up to Mr Corbyn’s plan.
She has agreed to meet the left-winger to discuss a no-deal prevention plan.
Mr Johnson has promised to take the UK out of the EU on October 31 with or without a deal.
The Prime Minister is demanding the controversial Irish backstop is scrapped before he meets the bloc’s leaders for negotiations on a new agreement.
