If the 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.
But speaking on the BBC’s Andrew Marr Show on Sunday, the Scottish First Minister said Theresa May had not revealed what her next plan for Brexit was - meaning extending Article 50 was “now pressing and urgent”.
Ms Sturgeon said: “I don’t think she had a clue herself where she’s going, if I can be as blunt as that.
“There’s an air of unreality. There’s almost an air of the Prime Minister and her Government being in complete denial about this. Yesterday there were reports in the media about how she might be close to getting a majority behind her deal by making a commitment to removing the backstop - ignoring the reality that the EU have shown no signs of being prepared to agree to that.
“That’s why I think now Article 50 should be extended, there should be a request made for that and the SNP were the first party to call for that.
“That is now pressing and urgent and SNP MPs on Tuesday this week will vote for Yvette Cooper’s amendment. We think that request should be made now, but nevertheless I think Yvette Cooper’s amendment takes us in the right direction.”
On Saturday the Scottish Constitutional Relations Secretary Mike Russell spoke at a Rally for Europe in support of a People’s Vote.
He said it would be “physically possible” to organise another referendum in the time available before the Brexit due date, however it remains one of the lesser considered options in Westminster.
When Ms Sturgeon was asked about its chances, she told Mr Marr: “I don’t think it’s off the table. I do accept that as things stand right now there doesn’t appear to be a majority in the House of Commons and that’s because for reasons that only he can or can’t explain, Jeremy Corbyn is fixedly on the fence on this issue. He said he wanted to try to get a general election, he tried that and failed.
“It seems to me it’s incumbent on Labour to make its position on this clear - if it does so then I do think there would possibly be a majority in the House of Commons so Labour, at the moment, are the block to that and I think that’s deeply regrettable.
“We’ll have to wait and see what Labour’s position would be. Firstly we’d have to wait and see if there would be a general election. It’s pretty inexplicable that Jeremy Corbyn and the Labour leader here in Scotland (Richard Leonard) doesn’t seem to be able to say what position on Brexit they would take in a general election.”
She added: “I’m simply recognising the many hypotheticals underlying. I’ve always said - I said in the 2015 general election if you recall, I said it in the 2017 general election - that the SNP would want to be part of a progressive alternative to a Conservative government if the arithmetic leant itself to that. That remains the case.
“Obviously Labour have to be willing to work with the SNP as well as the SNP being willing to work with Labour.
“Until now the blockage to working together like that has come from the Labour side but I would always do whatever I could as leader of the SNP to keep the Tories out of Downing Street.”