Conservative MP Ken Clarke has said he would not reject an offer to become caretaker prime minister if it was "the only way" to stop a no-deal Brexit.
Liberal Democrat leader Jo Swinson has suggested the ex-chancellor or former Labour deputy leader Harriet Harman could head a temporary government.
Mr Clarke told the BBC the idea was "not inconceivable".
But Prime Minister Boris Johnson has pledged that the UK will leave the EU by 31 October "do or die".
He has said he wants to strike a deal with Brussels, but if this is not possible, Brexit will go ahead as planned.
Meanwhile, Labour leader Jeremy Corbyn has said he plans to win a no-confidence vote in the government, become an interim prime minister, delay Brexit, call a snap election and campaign for another referendum.
However, some MPs have said Mr Corbyn does not have enough support in Parliament to enter Downing Street.
Lib Dem leader Ms Swinson has instead suggested Mr Clarke or Ms Harman - the longest-continuously serving male and female MPs - as alternative potential caretaker prime ministers, arguing that they command respect across Parliament.
Mr Clarke, a strong supporter of the EU who has three times run to become Conservative leader, told BBC Radio 4's PM he would "not object to" the idea 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.
He said that preventing a no deal through legislation could be the "best method" but added: "If that fails, you need a government of national unity... It is not a senseless suggestion."
Mr Clarke also said: "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 [when the world faced a large recession] 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."
He added that it would be a "single-issue, short-term government" that would seek an extension to the Brexit negotiation process.
Business Minister Kwasi Kwarteng said he was "a great fan" of Mr Clarke, but dismissed talk of him becoming prime minister as "speculation".
Mr Corbyn said he was "disappointed" by Ms Swinson's response to his plan, adding that he hoped she would "come round" to it.
"Under normal constitutional processes in Britain, when a government collapses, the leader of the opposition is called on to form a government," he said.
Mr Johnson has said the EU has become less willing to compromise on a new deal with the UK because of the opposition to leaving in Parliament.
He said this increased the likelihood of the UK being "forced to leave with a no deal" in October.
Mr Clarke was first elected to Parliament as a Conservative MP in 1970 for the Nottinghamshire constituency of Rushcliffe.
He held several senior government posts under Margaret Thatcher and John Major, including health secretary, education secretary and chancellor.
However, his pro-European stance put him at odds with many in his party and despite three attempts in 1997, 2001 and 2005, he failed to become Conservative leader.