She has told MSPs that the European Free Trade Association (EFTA) and European Economic Area (EEA) models are being looked at as the government explores ways of preserving Scotland’s links with the EU.
The EEA includes the existing EU states in addition to EFTA members Iceland, Liechtenstein and Norway.
Membership offers access to the single market.
However, members must make a financial contribution and adopt most EU legislation, including the free movement of people.
Ms Sturgeon has said she will publish proposals in the coming weeks which will be aimed at keeping Scotland in the single market even if the rest of the UK leaves.
Addressing a meeting of the Scottish Parliament’s conveners’ group, she said: “If the UK is intent on a hard Brexit and coming out of the single market, I want to look at how we could, and I’m not for a minute saying there wouldn’t be challenges associated with this, but whether we could find a way of protecting Scotland’s place in the single market.”