The Labour leader said the electoral process in the last general election needed to be respected, and that it should be the Opposition who are invited to form a government if a no-confidence motion in Boris Johnson’s administration succeeds.
But on a visit to Bolton, Mr Corbyn dodged the question of whether the likes of veterans Ken Clarke, of the Conservatives, or Labour's Harriet Harman would be less divisive figures to lead a unity government.
He said: “What we need is a respect for the electoral process that brought about the results from the last general election.
“What we need is a government that is prepared to negotiate with the European Union so we don’t have a crash-out on the 31st.
“This Government clearly doesn’t want to do that. Boris Johnson just wants to take us into the arms of the Americans and Donald Trump on a sweetheart trade deal.
“We are not going to do that. We will do everything we can to stop a no-deal Brexit.
“I am the leader of the Labour Party, Labour is the largest opposition party by far. That is the process that must be followed.”
Earlier Sir Oliver, who was among recipients of a letter from Mr Corbyn outlining his plan, said it was “well worth” having discussions across the Commons to prevent the UK crashing out of the EU without a deal.
But, when asked if he would make the Leader of the Opposition prime minister, he told BBC Radio 4’s Today programme: “That appears to be his agenda, I have to say it is not one I personally share.
“I don’t think it’s at all likely that a majority would be formed for that and I personally wouldn’t want to vote for it. I wouldn’t be able to support that, no.”
Fellow Remainer Dominic Grieve, who also received the letter, said that while he was willing to cooperate with Mr Corbyn, he did not think the Labour leader should be a caretaker PM.
“I simply don’t think that Jeremy Corbyn as leader of the Labour Party – particularly with his very strong views, which he is entitled to on a number of subjects – is the right person to do that,” he told the BBC.
Anna Soubry, leader of the Independent Group, confirmed on Friday that she would also “not support nor facilitate any government led by Jeremy Corbyn”.
But Mr Corbyn’s plan has won the potential backing of the SNP, Plaid Cymru and Tory MP Guto Bebb.
Meanwhile, a YouGov survey suggested that almost half of Britons – 48% – would prefer to see the UK leave the EU without a Brexit deal and Mr Corbyn not become prime minister, rather than him entering Downing Street and holding a second referendum.
The poll of 1,968 people taken between Thursday and Friday suggested just over a third – 35% – would, when faced with the choice, want the Labour leader to enter Number 10 and hold another referendum.
The remaining 17% said they were unsure either way.