The meeting at the SNP's Edinburgh headquarters is likely to focus on the party's commitment to a referendum on Scottish independence within the next four years, a policy that the Lib Dems have openly opposed.
Alex Salmond, the SNP leader, has attempted to tempt the Lib Dems into the fold with suggestions that he would be willing to compromise by giving the Scottish people a range of options in any public vote with their preferred model of increased powers of the existing parliament included.
However, speaking at a gathering of supporters in the city's Royal Mile, he also warned that it was necessary that other parties take note of the success of the SNP and the appeal of their policy.
"Let's give the people, perhaps people who haven't done as well as we have in this election, time and space to have a think about this because I'm sure everybody wants to respond to the message of the electorate. I'm certainly prepared to do that, I think others will do as well," he said.
The Liberal Democrat leader in the country, Nicol Stephen, felt the effects of the electorate's swing behind the SNP as his Aberdeen South majority was cut to 2,732.
Despite reservations over a possible move to independence, his determination not to abuse his power as a critical minority in the parliament may convince him to find an agreement with Mr Salmond.
"I'm not the kingmaker here. It's not me that will decide, it's the Scottish electorate," he said on retaining his seat.
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