The First Minister said the SNP would push for Brexit to be halted by revoking Article 50 to avoid a no-deal exit.
With ‘indicative votes’ on Brexit alternatives set to be held in the House of Commons, Ms Sturgeon said a single market and customs union deal to leave the EU was “not our first preference”.
“At the moment, I think the option of remaining is not off the table and it's not beyond the bounds of possibility by any stretch of the imagination,” she said.
Ms Sturgeon added: “I would like to see article 50 revoked. That would be preferable to crashing out with no deal.”
Speaking to the BBC’s Andrew Marr show shortly before joining a 1m-strong march through London for a second EU referendum on Saturday, Ms Sturgeon also backed a so-called People’s Vote.
“The government has absolutely failed to deliver on the result of the 2016 referendum.
“They have no credible way forward now and when parliament and government fails, it seems to me that the only sensible thing to do is put the people back in charge.”
Reports suggest the Prime Minister could be ousted by her cabinet as soon as Monday with Conservative MPs in open revolt over plans for indicative votes and a deal to delay Brexit by at least two weeks.
“I’m telling her to go,” Ms Sturgeon said. “I think she’s been part of the problem for some considerable time.
“I think if we were in any normal period in British politics, she would be long gone.”
The First Minister added: “I think she is effectively out of power right now, and I think debating her position is becoming more and more incidental by the day.
“What’s important now is that the House of Commons seizes control, and does so next week.”
Ms Sturgeon did not clarify when she would set out plans for a second Scottish independence referendum, which have been promised for the past six months.
“I think another Scottish independence referendum is going to happen,” she said.
“Before I set out a path forward for Scotland I think it’s reasonable for me know what the starting point for that journey is going to be, and the context in which we're going to be embarking on it.
“We need to know, and hopefully we’re going to know this in the next few days, and the next three weeks: is the UK leaving the EU, is it leaving with a deal, is it leaving with no deal; or is it not leaving at all, perhaps looking at another [EU] referendum.
“But the experience of the last three years, Scotland’s vote ignored, the voice of the Scottish Parliament ignored, all of the consequences that flow from Brexit completely outwith our control, that really does make the case for independence very, very powerfully.”