Nicola Sturgeon has said she believes Scotland could stay in the European single market if other parts of the UK leave.
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.
Ms Sturgeon also criticised the Prime Minister for holding "secret" Brexit negotiations.
Speaking on ITV's Peston on Sunday programme, the SNP leader said that Theresa May refusing to share her negotiating position on Brexit with the public or the House of Commons is "unacceptable".
She added: "The House of Commons and the wider public has almost been told to butt out and mind their own business, and we saw in the House of Commons last week there's not a lot of support for that kind of approach.
She said it was not acceptable to have a "secret negotiating strategy" and it should be shared with the public and endorsed by parliament.
At the SNP conference earlier this week the First Minister pledged that the Scottish Government will call a second independence referendum if the UK opts for a so-called "hard Brexit" but said she wants to work with others to try and "save" the UK from being removed from the single market.
While the UK as a whole opted to leave the European Union in June's referendum, 62% of Scottish voters backed remain, with Ms Sturgeon saying this then made another vote on independence "highly likely".
She has already said the Scottish Government will publish a draft independence referendum bill for consultation next week.