Sturgeon said a vote is "common sense" considering the United Kingdom's decision to leave the European Union within the next few years. Scots overwhelmingly voted to remain in the EU during the Brexit referendum last June.

"I guess when the sort of outline of a UK deal becomes clear on the UK exiting the EU, I think that would be a common sense time for Scotland to have that choice if that is the road we choose to go down," Sturgeon said in a BBC interview aired Thursday.

Scots last voted on independence in 2014, when 55 percent voted to stay in the U.K. A poll released Thursday shows more Scots are coming around to the idea of independence. A slim majority, 51 percent, still wants to remain in the U.K.