In a speech in Edinburgh, the Scottish National Party (SNP) leader cited continuing access to the EU single market and maintaining freedom of movement with the bloc as two things that were key to Scotland's economic interests.
But she said the British government appeared to be "heading towards a 'hard' rather than a 'soft' Brexit, a future outside the single market with only limited access and significant restrictions on free movement".
British Prime Minister Theresa May has said she will not trigger Article 50 of the EU's Lisbon Treaty, which starts the two-year countdown to Brexit, before the end of the year to give time to consult with all nations in the UK.
As well as economic concerns, Scotland also wanted to preserve EU social protections and international alliances on crime and climate change, she said.
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"At this stage we must keep all of our options open," Sturgeon told a meeting organised by the IPPR think tank.
In the coming months "the (UK) nations that voted to leave can start figuring out what Brexit actually does mean, while others like Scotland can focus on how to retain ties and keep open channels that we do not want to close or dismantle".
"Protecting Scotland's interest is my starting point and I am determined to explore all options to do that," she said.
"But if we find our interests can't be protected in a UK context, independence must be one of those options."
Sturgeon mentioned in passing a theory described as "Reverse Greenland", that would see England, Wales and possibly Northern Ireland leave the EU but Scotland stay, taking on Britain's membership.
Greenland, part of the Kingdom of Denmark, left the European Economic Community in 1985 while Denmark stayed in.