Scotland’s First Minister said it would be “challenging” but “possible” and that detailed proposals would be published within weeks.
Speaking on the BBC’s Andrew Marr show, Ms Sturgeon said: “We are going to put forward proposals, that we would hope that the UK Government would be prepared to listen to, that would allow Scotland to preserve its place in the single market and preserve aspects of its relationship with the EU.”
She went on to accuse Theresa May of “not fully honouring” promises to listen to Scotland on Brexit made on a visit to Edinburgh days after becoming Prime Minister.
Ms Sturgeon said: “Theresa May came to Edinburgh just a couple of days after she became Prime Minister, gave a commitment to me and to Scotland that we’d be fully involved and that she would listen to options we put forward.
“I think it’s fair to say that promise hasn’t been fully honoured and I hope we’ll see it honoured in the days to come.”
Ms Sturgeon said the situation was “frustrating” and added: “What I’m trying to do is to explore options whereby Scotland doesn’t have to leave the European Union or the single market, because we voted to stay in.
“There’s a fundamental principle here about, does Scotland’s voice matter? Does what we say, how we vote, how we think, count for anything?”
The First Minister, who is due meet the Prime Minister along with the leaders of other devolved administrations next Monday, called on Mrs May to demonstrate that Scotland’s voice does matter and that Scotland’s interests can be protected during Brexit negotiations.