Scots have “a part to play in a growing, strengthening, winning campaign across the UK” to stay in the EU, Ms Swinson will tell Lib Dem delegates in Bournemouth today.
In his own speech to the conference, Scottish Liberal Democrat leader Willie Rennie will say Scots “don’t have to cut and run with independence” to stop Brexit.
The calls will come after criticism and accusations of hypocrisy after the Lib Dems made it their policy to revoke Article 50 and cancel Brexit if they win a majority in a snap election – despite pledging to oppose a second independence referendum even if the SNP wins a Scottish Parliament majority.
“I want to speak directly to people in Scotland,” Ms Swinson will say this afternoon. “We together voted overwhelmingly to remain in the European Union and together we can stop Brexit.
“We are building a movement across the United Kingdom that is on the verge of stopping it.
“You have a part to play in a growing, strengthening, winning campaign across the UK. Join us.
“Come with me and be part of the bigger movement for change. A big vote for the Liberal Democrats in Scotland at the general election will give us the final push that we need.
“The energy is with us. Come with us to stop Brexit.”
Adding to expectations of a Lib Dem breakthrough after the party added seven defecting MPs in six weeks and, with an election looming, Ms Swinson will make a pitch to form the next government.
“The tired old parties have failed, looking inward at a time of national crisis. Our country needs us at this precarious time,” she is expected to say. “We do not have ten or 15 years. We need to seize the opportunity now ... and today I am standing here as your candidate for prime minister.”
Ms Swinson will also accuse Boris Johnson of “doing a pretty good impression” of a “socialist dictator” by purging rebels from his party, and claim Jeremy Corbyn is part of the “collective forces of nationalism and populism” alongside the PM and Brexit Party leader Nigel Farage.
The Lib Dem leader was forced to defend her party’s new policy of cancelling Brexit after some of her MPs warned it was “incredibly dangerous” and undemocratic.
“I don’t feel personally that there are enough people out there trying to find ways to reunite our country,” Sir Norman Lamb told the BBC yesterday.
“I think that the polarisation that we are seeing is incredibly dangerous. I think we are playing with fire in many ways.”
Mr Rennie defended his party’s stance of pledging to block another independence referendum even if there is majority support at Holyrood after the next election, and claimed voters switching to support the break-up of the UK “don’t really want independence”.
He said he had been consulted before the move was announced a fortnight ago, amid complaints from some Lib Dems that the policy had taken them by surprise.
“With the rise in support for independence, a lot of that is coming from Remainers, and they are desperate to stop Brexit,” Mr Rennie said.
“Just now they’re flirting with independence and the SNP. We speak for those people.”
The Scottish Lib Dem leader insisted that “to keep the status quo, you just need a mandate through the ballot box at a general election”.
He added: “We recognise that [the 2016 referendum] happened, but people have had enough of Brexit and we want to bring it to an end ... if you’re going to have ‘Big Bang’ constitutional change, you absolutely need to be sure you’re going to get the people to back it.
“Stopping it is another matter.”
Scottish Conservative leader Jackson Carlaw compared the Lib Dems to the SNP for rejecting the result of a referendum, saying Ms Swinson was “taking her party into dangerous territory”.
“No matter which side you campaigned for, political parties should respect the result of referendums,” Mr Carlaw said.
“But, just like Nicola Sturgeon, Jo Swinson and Willie Rennie are now saying that they get to pick and choose which referendums should be honoured and which should be ignored.”