Ms Friis, who served as climate, energy and gender equality minister between 2009 and 2011 and is now the head of Think Tank EUROPA, told Dr Kirsty Hughes, director of the Scottish Centre on European Relations: "From the public opinion point of view that would be popular.
"Scotland is also sometimes seen as a northern country, you could strike an alliance to that."
The Nordic Council is the body for formal inter-parliamentary cooperation among the Nordic countries such as Denmark, Finland and Norway.
Since the Brexit referendum, the Scottish Government have renewed their calls for independence and vowed to rejoin the EU if independence is won.