The group has been pushing for a fresh vote on whatever exit plans result from talks with EU leaders.
Theresa May has rejected calls for a such a vote, while Labour has said it wants a general election to decide the issue.
SNP leader Nicola Sturgeon has cleared the way for party MPs to back a second EU referendum.
Scotland voted 62% in favour staying in the EU in 2016, with all 32 council areas backing Remain, but the overall UK vote was 52% in favour of leaving.
Former UK transport secretary Lord Adonis is in Edinburgh on Saturday for at an event organised by “Our Future Our Choice” to examine the Brexit impact on young people.
He will challenge Scottish Labour to “get off the fence”, while the panel at the event will also call on Scottish Conservative MPs to back a People’s Vote.
He said: “Scotland’s MPs will be critical in the fight for a People’s Vote.
“Scotland voted overwhelmingly to Remain, so the Scottish Labour Party must get off the fence and back a People’s Vote.
“The vast majority of Labour Party supporters in Scotland want one, and they do not want their only pro-EU option to be the SNP.”
Edinburgh MP Ian Murray and MEP Catherine Stihler will also speak at the event in George Square, titled What next for Brexit?
Mr Murray said Scottish Tory MPs need “to stop acting as Lobby fodder for the Brexiteers, and get behind a People’s Vote”.
Ms Stihler said: “Brexit threatens the opportunities for young people from across Scotland.
“We must do everything we can to give people an opportunity to prevent Brexit, and there are tens of thousands of youngsters who didn’t get a vote in 2016 who back a People’s Vote.
“Future generations will not forgive us if we go ahead with Brexit.”
The Liberal Democrats back the People’s Vote campaign, and MSP Tavish Scott has called for Scottish Labour politicians to do the same.
He said: “We know a sizeable majority of Labour supporters in Scotland don’t agree with the party’s pro-Brexit policy. Polls show they back a vote on the deal and want to stay in the EU.
“Kezia Dugdale and Ian Murray back a vote on the deal. Are there no other Scottish Labour politicians willing to do the right thing and join the Liberal Democrats in campaigning for people to have the final say, and the opportunity to Exit from Brexit?”