The stark claim was made by Scottish Conservative MSP Murdo Fraser who says that Mrs Sturgeon will not stop until she gets what she wants.
Mr Fraser said: "She may have been reluctant to say it out loud, but eventually Nicola Sturgeon conceded she wants to see Jeremy Corbyn in Downing Street ahead of Theresa May.
"That paves the way for an allegiance in Westminster between Labour and the SNP that would all but guarantee another divisive referendum on independence.
Nicola Sturgeon wants Jeremy Corbyn in Downing Street instead of Theresa May
"That's not what Scotland wants, and proves only one party can be trusted to keep Scotland as a key part of the UK."
In March, Ms Sturgeon, the leader of the Scottish National Party (SNP), announced her intention to hold a second vote between autumn 2018 and spring 2019, but this was rejected by Mrs May.
She has continued to push for a second Scottish independence vote, claiming the nation was being forced into leaving the EU because of England.
Conservative Murdo Fraser says that Mrs Sturgeon will not stop until she gets what she wants
Mrs May has said that she would not consider a referendum until after Brexit.
However, her repeated requests have been shot down by the Prime Minister.
In the Conservative Party's General Election manifesto, one of Mrs May's key election pledges is of “a strong and united nation” and the Tories vowed to delay the First Minister’s bid for a Scottish independence.
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The manifesto said: “A strong and stable Union, with no divisive Scottish referendum at this time.
“The United Kingdom has voted to leave the European Union but some would disrupt our attempts to get the best deal for Scotland and the United Kingdom with calls for a divisive referendum that the people of Scotland do not want.
Ruth Davidson has also vowed to stop Nicola Sturgeon's bid for a second referendum
“We have been very clear that now is not the time for another referendum on independence.”
"In order for a referendum to be fair, legal and decisive, it cannot take place until the Brexit process has played out and it should not take place unless there is public consent for it to happen. This is a time to pull together, not apart."
Ruth Davidson has also vowed to stop Nicola Sturgeon's bid for a second referendum on Scottish independence.
The Scottish Tory leader said the prospect of Jeremy Corbyn in Number 10, with John McDonnell as his chancellor and Diane Abbott as home secretary, would focus voters' minds.
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She spoke out with less than two weeks to go until the June 8 General Election, with several polls showing the Conservative lead shrinking, including one which put Theresa May's party just six points clear.
An ORB poll for the Sunday Telegraph had Tories down two points in the past week on 44 per cent, six points ahead of Jeremy Corbyn's Labour on 38 per ent (up four points).
That equals Labour's best rating since Mr Corbyn became leader and would see him comfortably outpoll Ed Miliband and Gordon Brown's election results if repeated on June 8.
Ms Davidson told the Sophy Ridge on Sunday programme on Sky News: “Theresa May is Prime Minister, I hope she continues as Prime Minister, in three weeks' time the first day of negotiations for Brexit are going to happen and we will either be led by Theresa May of Jeremy Corbyn.
"And I absolutely, seven days a week, twice on a Sunday, think Theresa May is the best person in that job.”