Last week, Mr Corbyn wrote to senior opposition MPs outlining plans to call a vote of no confidence in the government in the autumn.
The Labour leader would lead a “time-limited” government which would extend Article 50 and call a general election under the proposals.
However, the plan was met with fierce opposition from the Liberal Democrats, with leader Ms Swinson saying Mr Corbyn was too divisive to lead a national unity government.
She suggested senior Tory and Labour backbenchers Ken Clarke and Harriet Harman take the helm instead.
“The Liberal Democrats have been working with others for years in the national interest, because we know that together we can stop Brexit. I look forward to meeting with other leaders to discuss how we can stop the disastrous consequences of no-deal,” Ms Swinson said in a statement.
“We must focus on workable options that can actually stop no-deal Brexit, because we do not have time to waste.
“If Jeremy Corbyn truly wants to stop no-deal, then he must be open to options other than his plan to become prime minister and I look forward to hearing about the different options he is willing to explore.”
James Cleverly MP, Conservative Party chairman, also responded to Mr Corbyn’s letter.
He said: “Jeremy Corbyn will do all he can to stop delivering on the referendum result.
“The alternative to delivering Brexit is Jeremy Corbyn as prime minister, a man who would wreck the economy, is soft on crime and won’t stand up for Britain. All Jeremy Corbyn offers is more dither and delay.
“Only Boris Johnson and the Conservatives can provide the leadership Britain needs and deliver Brexit by 31 October, whatever happens.”