Scotland's Deputy First Minister John Swinney would not dismiss the idea, despite being asked repeatedly in an interview if the SNP would pursue it.
It comes after the party's leader in Westminster Angus Robertson accused the Tories of being too “scared” to allow an official second referendum to take place, following Ms May’s claim that “now is not the time” to have another vote.
Asked on BBC Radio 4's Today programme if, as a result of the Prime Minister's refusal, an unofficial vote was a plan, Mr Swinney said: “If Theresa May takes that stance she will be standing in the face of Scottish democracy and that is a very, very unstable and dangerous position for the Prime Minister to be in.”
Pressed further, he said: “What we will do, is, we will discuss this issue with the Scottish parliament, we will debate it in the course of this week, we will get to the conclusion of that debate. I’m confident the Scottish parliament will demand the right to start the process of having an independence referendum and it will be up to the Prime Minister to recognise the democratic wishes of the the people of Scotland.
“If she doesn’t she’ll be turning the clock back to the bad old days of the times when the Conservatives ignored democratic opinion in Scotland.”
Earlier this week SNP leader Nicola Sturgeon set out her intention to push for another referendum and she is likely to ask the Scottish parliament to vote on it next week. But on Thursday, Ms May said “now is not the time”, with aides indicating no vote would be permitted before Brexit.
Speaking at the SNP's spring conference in Aberdeen, Mr Robertson was to say today: “It is clear from the PM’s panicked response to the Scottish Government’s decision to rightly, give people in Scotland a choice over Scotland’s future, that the Tories are simply scared of the people’s choice.
“The Tories argument is not about process, it is about their desperate desire to prevent anyone having the chance to reject the hard-right Brexit that they are so wedded to.”
His words come as Ms May prepares to speak at her party's spring conference in Cardiff and after she wrote in The Times this morning claiming the SNP wants “to force” the UK Government into agreeing to a referendum that would be unfair to the Scottish people.
Explaining her position she wrote that another vote “is not something to which any responsible government could reasonably agree”.
She added: “The SNP is trying to force the UK Government to agree to something that is fundamentally unfair to the Scottish people. It wants to ask them to make a crucial decision without the necessary information.
“They would not know what the new partnership with the EU would look like, or what the alternative of an independent Scotland would be. It would simply not be fair.”Reuse content