During the interview with Andrew Marr, Ms Sturgeon also confirmed that the SNP would back a bid by Labour MP Yvette Cooper to postpone Brexit Day.
If Ms Cooper’s amendment is selected by the Speaker, MPs will vote on whether the prime minister must seek a delay to the planned Brexit date of March 29 if no deal has been approved by February 26.
SNP Westminster leader Ian Blackford is also expected to table an amendment on Monday calling on Mrs May to note the Scottish Parliament, Welsh Assembly and Commons all voted “overwhelmingly” to reject her deal.
Ms Sturgeon said extending Article 50 was “now pressing and urgent”.
“No, not really,” Ms Sturgeon said. “I don’t think she has much of a clue herself where she’s going, if I can be as blunt as that.
“It looks to me that she’s putting all her eggs in one basket of trying to convince the hardliners and the DUP, the ERG to do what they weren’t prepared to do a few weeks ago and back her deal.
“There’s an air of unreality, there’s almost an air of the prime minister and her government being in complete denial about this.”
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Your guide to Brexit jargon
Sturgeon on Scottish independence
During her speech to the SNP party conference in October, Ms Sturgeon told supporters she would “wait for the fog of Brexit to clear” before outlining her plans for another vote on Scottish independence.
Pressed on the issue during her BBC interview, she said she wanted to see how the Brexit issue unfolded over the coming weeks before outlining her plans.
“I think the people of Scotland should have the opportunity to look again at independence,” she said.
“The material change in circumstances since the last referendum, our experiences over the last two-and-a-half years – not just facing exit from the EU and being taken out of the single market against our will with damaging economic consequences but our views being ignored – I think make that important.”
She was asked if she would call for another Scottish referendum if the UK left the EU without a deal.
She replied: “Within that timeframe of when the UK is leaving. So if the UK is leaving at the end of March – we don’t yet know whether that will be the case, we don’t know whether it will be with a deal or without a deal – but within that timeframe yes, I think I’ve been pretty clear that is when I would intend to set out my views on the way forward for Scotland.
What are the opposition saying?
Jackson Carlaw, the Scottish Conservative’s interim leader, described Ms Sturgeon as “evasive” in the interview.
“No matter what happens within her own party or elsewhere, she won’t stop banging on and on about her campaign for another independence referendum,” he added.
His comments came after Prime Minster Theresa May outlined her opposition to the issue in weekly questions in the House of Commons last week.
She said: “The last thing we want is a second independence referendum. The United Kingdom should be pulling together, and should not be being driven apart.”
Meanwhile Willie Rennie, the leader of the Scottish Liberal Democrats, urged the the SNP government to “park the issue of independence” and concentrate on getting its budget through the Scottish Parliament.
As the SNP does not have a majority at Holyrood, it needs the support of at least one other party if the financial package is to be approved. But talks between the SNP and the Scottish Greens have stalled over concerns about funding for local government.