In response, Mr Corbyn plans to hold a no-confidence vote "at the earliest opportunity" and if successful will seek to form a caretaker government on a "strictly time-limited" basis.
"There is a bad kind of collaboration as it were going on between those who think they can block Brexit in parliament and our European friends", Johnson, who has been hailed by the USA president as "Britain's Trump", said on Facebook.
And, four senior lawmakers who are opposed to a no-deal Brexit are open to discussing the leader of the opposition's plan to try to bring down Prime Minister Boris Johnson, Sky News reported on Thursday.
Mr Corbyn is certain to face opposition from some Conservatives in government and Brexiteers, but some Remainers have also signalled that they are less than impressed with his offer to become interim prime minister, sidelining Tory Remainers and the pro-EU Liberal Democrats.
Many economists and businesses say a no-deal Brexit will cause economic turmoil, and Johnson's critics accuse him of steering the country off a cliff.
Johnson, in turn, alleged that anti-Brexit UK politicians were collaborating with the European Union to block Britain's exit from the bloc.
Yesterday, Ms Swinson told BBC radio she had spoken to both of them, and both said they would be willing to serve.
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"If Parliament does not back that, then it's for whoever can command the confidence of the house".
Jo Swinson, the party's new leader, does not think he is the right man for the job.
Germany expects a No Deal Brexit and is not prepared to renegotiate the withdrawal agreement, according to leaked details of an internal briefing paper for Angela Merkel's government. "To set the bar for negotiations so high that we inevitably leave without a deal would be a betrayal".
If that vote succeeds, he says he wants Parliament to put him temporarily in charge, so that Brexit will be delayed and a general election can take place.
He said he hoped his proposal to lead a caretaker government could "halt the serious threat of No Deal, end the uncertainty and disarray, and allow the public to decide the best way ahead".
Mr. Corbyn, a low-key Remain campaigner during the 2016 referendum, has been under pressure within his party to step up efforts to prevent it from happening. The Greens' Caroline Lucas confirmed she would back a vote of no confidence but asked Corbyn to support a different MP as leader of a temporary government if he can not win the confidence of the House himself.
Meanwhile Commons Speaker John Bercow promised to "fight with every breath in my body" to prevent Mr Johnson from proroguing Parliament in order to achieve a no-deal Brexit. Neither has Nick Boles, the independent MP who quit the Conservatives over Brexit and who also received the appeal.