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 House of Commons had to “find a way” forward.
Prime Minister Boris Johnson has pledged that the UK will leave the EU by 31 October “do or die”.
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 become prime minister.
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, saying they were both experienced and 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: “I wouldn’t reject it if it was the only way forward.”
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.
Ken 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.