Scotland's First Minister Nicola Sturgeon has told Sky News the Prime Minister's opposition to a second independence referendum is "unsustainable".
"The coming negotiations with the European Union will be vital for everyone in the United Kingdom", she will say.
The former first minister reportedly said that independent Scotland could have the same flexible border with the rest of the United Kingdom as May promised for Northern Ireland and Ireland.
Responding for the government, Scottish Office Minister Lord Dunlop confirmed that the prime minister was ruling out another referendum in Scotland, and he also stated that the Secretary of State for Northern Ireland, James Brokenshire MP, had ruled out a border poll on the grounds that the terms for such a poll are set out in the Belfast Agreement and such conditions are not met.
With Scottish Tory officials confirming May could have to authorise a referendum if Scottish public opinion demanded it, Sturgeon and her aides have also indicated she could be more flexible on dates.
The Conservative-led British government, however, must agree to a legally binding referendum and May said "now is not the time".
Asked a fourth time by host John Humphreys, he said: 'If Theresa May takes that stance she will be standing in the face of Scottish democracy'.
A spokesman said May hoped the Scottish parliament would back away from staging a vote.
In her heart, in her political DNA, the idea of an independent Scotland will always shine, and that after all is the core objective of her party, but her stated ambition - to leave the United Kingdom and cling to the European Union - should instead be in her party's manifesto and be put to the Scottish people at the next general election. The two parties hold a combined majority in the parliament.
Scottish Conservative leader Ruth Davidson, whose party has the second-largest bloc of seats, said the Tories would oppose the push for a new independence vote.
May, appointed prime minister soon after Britain voted to leave the European Union in a referendum last June, said she would negotiate a Brexit deal for the whole country but needed everyone to pull together to get the best outcome.
Brexit Secretary David Davis said Mrs May would formally invoke Article 50 by the end of March, allowing the United Kingdom to start talks on creating a "positive new partnership" with the EU.
Minutes after Sturgeon called on Monday for a new referendum, Scottish National Party activists start putting up bunting left over from the 2014 campaign, in Paisley, Scotland.
The Scottish Greens, another pro-independence party, said May risked boosting support for independence if she wanted to veto a decision expected to be made by Scotland's devolved parliament next week. Areas like Paisley have long supported Scottish bids for independence.
But EU negotiators warn it could take two years just to settle the divorce terms, and agreeing on a new relationship for the United Kingdom and the EU could take years longer.