SNP strategists are believed to be considering introducing a referendum bill at Holyrood to keep up pressure on the UK government and draw out the dispute over the right to hold a second vote.
The move would force UK ministers to take the Scottish Government to the Supreme Court to strike down the legislation if the Prime Minister continues to refuse permission for a second referendum.
The Scottish Government cannot call a referendum without reaching an agreement with Downing Street on a Section 30 order under the Scotland Act, giving it power to legislate on constitutional matters reserved to Westminster.
Mrs May insists no talks on a referendum will take place until after the Brexit process is complete, having told the SNP that “now is not the time”.
Nicola Sturgeon has said she will reveal her “idea” of how to “progress the will of parliament” after Easter.
The Presiding Officer of the Scottish Parliament can rule on whether legislation put forward falls within Holyrood’s legal powers, but bills can proceed even if they are deemed to be outside its competence.
Under Section 33 of the Scotland Act, once legislation is approved by MSPs, there is a four-week period before it receives Royal Assent where the UK’s law officers can refer all or part of the bill to the Supreme Court to have it struck down.
In 2015, a bill proposing to ban pavement parking was introduced despite confusion over whether Holyrood or Westminster had the power to legislate.
Despite a ruling from the Presiding Officer that the bill covered a reserved matter, it progressed and was passed as normal. The necessary powers were later devolved as part of the Scotland Act 2016.
Constitutional experts differ over whether the First Minister could force the issue using Holyrood legislation.
Tobias Lock, a senior lecturer in EU law at the University of Edinburgh, said the SNP “could call an independence referendum if they can get it through the Scottish Parliament and it’s not thrown out by the Presiding Officer”.
But Vernon Bogdanor, one of the leading experts on the UK constitution and an emeritus professor at the University of Oxford, said there was no way a referendum could be held without Westminster approval. “I can’t see what the Scottish Government could do if the UK Government said no to a referendum,” he was quoted as saying.
“There’s been talk that they could hold their own referendum, but they could face a legal challenge or they could get a petition asking that the power to hold a referendum be transferred and it might put pressure on the UK Government.
He said: “Ultimately the power to call a referendum is a UK Government power and not a Scottish Government power.”
A Scottish Government spokesman did not rule out the idea of pushing legislation through Holyrood, insisting there was a “cast-iron democratic mandate” to hold a second referendum following the Brexit vote.
He added that blocking a referendum “indefinitely” would be “utterly undemocratic and unsustainable”
Conservative MSP Murdo Fraser said a bid to pass a referendum bill without a Section 30 order in place would represent “cynical gesture politics”.