Speaking on the Andrew Marr Show, she said the UK leaving the EU need not entail Scotland being excluded from a separate trade arrangement.
"I think that is possible," she said.
The first minister said her government was looking at the detail of how that could happen, adding: "We will publish proposals over the next few weeks."
Ms Sturgeon told the programme her first approach would be to support an acceptable trade deal for the whole of the UK.
She said: "We are going to work with others across the political divide to avert a hard Brexit not just for Scotland but for the whole UK.
"I don't believe there is a mandate to take the UK out of the single market and I don't believe there is a majority in parliament."
The first minister denied she was underestimating the difficulties of finding a solution which allowed Scotland to retain access to the single market if the UK as a whole chose to leave.
"I don't suggest for a second that would be straightforward or without challenges," she said.
"But in the unprecedented circumstances we're in just now, I think there's an obligation on all of us to try to work out solutions that will allow the vote in Scotland to be respected, just as I understand that Theresa May wants the vote in other parts of the UK to be respected."
During Ms Sturgeon's speech to the SNP conference on Saturday, she set out a four-point plan to boost Scottish trade and exports. This would include:
She told party members: "Let me be crystal clear about this - Scotland cannot trust the likes of Boris Johnson and Liam Fox to represent us.
"They are retreating to the fringes of Europe. We intend to stay at its very heart where Scotland belongs.
"We are in a completely new era. A new political era and a new battle of ideas.
"A new era for our parliament, with new powers and responsibilities, and a new era for our relationship with Europe and the wider world."
First Minister Nicola Sturgeon has said she believes a deal could be reached which would allow Scotland to retain access to the European single market.