The Scottish First Minister said she will approach the negotiations with “an open mind” and put “all options on the table”.
But she confirmed a second Scottish independence referendum is on the table - and relegated any option short of full EU membership to “second, third or fourth best”.
She told BBC News her first priority is “to make sure that Scotland’s place in Europe is close to the top of the busy agenda that (Mrs May) now takes over”.
She added: “We will want to get a very firm assurance from Theresa May that Scotland and the Scottish Government will be centrally involved in the process that will now take shape.
“But also that we will be able to be involved for a purpose - and that purpose will be to enable different options of allowing how Scotland voted to be given effect to be examined.”
Ms Sturgeon said she does not underestimate the difficulties of keeping Scotland in the EU, after voters in Scotland who backed remaining in the EU were outvoted by those in England and Wales.
She was asked if she would be comfortable with a deal that gave the UK access to the single market with some restrictions on freedom of movement.
She said: “Obviously we have to wait and see how these discussions take shape, but my starting point of principle is Scotland voted to stay in the EU.”
She added: “All options are on the table so I go into these discussions with an open mind - but based firmly on that point of principle.”
Ms Sturgeon told Sky News that a second referendum is “of course one of the options that needs to be on the table”.
She said: “It’s not my starting point - my starting point is how we best protect Scotland’s interest - so all options have to be on the table.”
Ms Sturgeon was critical of any option that would give Scotland access to the single market outside of the EU.
“Why take years and years to negotiate outcomes that are second, third, fourth best when we have a situation right now in which we have access to all of these things already,” she said.
“I want to protect what Scotland already has.”
Ms Sturgeon said Scotland can remain in the EU after the UK leaves.
“I’m not pretending that this route forward will be easy and we will face a lot of challenges,”, she said.
The EU has strict economic criteria for accession states, including a requirement to avoid excessive deficits.
Ms Sturgeon said “Scotland has got a fundamentally strong economy” but acknowledged “we’re facing a situation in the UK where the economic prognosis is not particularly positive”.
She added: “The UK, because of this decision, may end up going into recession but I hope that doesn’t happen.”
When asked if it would be in Scotland’s best interests to join the euro, she said: “No, of course I have never argued for us to join the euro.
“Sweden joined the EU after the obligation to join the euro was in force and Sweden, it is commonly accepted, will not join the euro unless it wants to.
“So I don’t argue for euro membership, and I don’t think euro membership comes as a necessity of EU membership.
“We will make decisions about currency if we are in the position of being independent that are in the best interests of the country, but we should accept positions that are inaccurate in terms of what would be required and what wouldn’t be required.”