Theresa May reportedly fears the Scottish government will call another independence referendum around the same time she triggers the formal Brexit process under Article 50 next month.
According to The Times, the UK Government is preparing for Nicola Sturgeon to use the start of the country's exit from the European Union to call another vote on Scottish independence.
Mrs May could reject it and risk a constitutional crisis or accept it and potentially imperil the future of the United Kingdom.
She has promised to trigger Article 50 by April and expects to be able to stick to the timetable, despite ongoing parliamentary wrangling over the process.
The report came as the Prime Minister urged voters in Scotland to use May's council elections to make clear to First Minister Ms Sturgeon that they do not want to have another independence referendum.
Ever since the UK voted to leave the EU but Scotland voted to stay in, there has been speculation that the Scottish government will seek to hold another referendum.
Ms Sturgeon has warned that Mrs May's plans for a hard Brexit, taking the UK out of the single market, "undoubtedly" made that a more likely prospect.
But writing in Holyrood magazine, the Prime Minister said her party would be "looking forward to the local elections in May, when voters across Scotland will have the chance to send a clear message to the SNP that they do not want a second independence referendum, by voting Scottish Conservative and Unionist".
Meanwhile, Scottish Labour has launched a dedicated website TogetherStronger.scot, where people can register their objection to a possible second independence referendum.
Leader Kezia Dugdale called on people to do so if they "believe that our country is already divided enough" and that the First Minister should "shelve her plans for a second referendum".
An SNP spokesman said: "There is already a cast-iron democratic mandate for an independence referendum - that was delivered in last year's Holyrood election, however much the Tories might try to deny it.
"That mandate also stems from the EU referendum, which saw Scotland vote by a 24-point margin to stay in Europe - and Theresa May's reckless pursuit of an economically ruinous hard Brexit will only strengthen opinion in Scotland against leaving Europe.
"The Prime Minister couldn't be more wrong to suggest there is considerable common ground between her Government and the Scottish government on Brexit - her party is hell-bent on taking us out of the world's biggest single market, with all the economic damage that would cause, while we are intent on protecting Scotland's vital national interests."