"There is no economic case for breaking up the United Kingdom, or of loosening the ties which bind us together".
Scottish Secretary David Mundell said that while a second independence referendum was possible, it was not the right course for Scotland.
Speaking to talkRADIO, he said: "Theresa May pays no attention whatsoever to Scottish politics, but we know she's anxious about the idea of independence".
The Scottish government have stated that they would need to seek approval from Westminster before holding a second referendum.
Since last year's Brexit vote, Scottish National Party leader and Scottish First Minister Nicola Sturgeon has repeatedly said she could push for a new independence referendum if the country is forced into a clean break with the bloc.
She accused nationalists of "neglect and mismanagement" of education, "abysmal failure" on farm payments, "starving the health service", and replacing stamp duty with a tax which costs home buyers more but brings in less revenue than expected.
"A party resolutely focused on just one thing: independence".
Mrs May said was determined to achieve a Brexit deal which "works for all parts of the UK - England, Scotland, Wales and Northern Ireland - and for the United Kingdom as a whole".
She implied the entire devolution settlement of 1998, which set up the Scottish parliament and Welsh assembly, was now up for renegotiation, risking a furious row with the Scottish government.
Ahead of the PM's speech, Sturgeon told Bloomberg: "The Scottish government's approach since the European Union referendum has been to offer compromise and to seek consensus at every turn".
Scotland may not be given control over key policy areas such as fishing and agriculture once the United Kingdom leaves the EU to avoid undermining the "coherence and integrity" of the Union, the i newspaper quotes the prime minister as saying.
While there has been no official statement from United Kingdom officials in this late hour on Sunday, the prospect of even more politcal chaos, not to mention the sudden possibility of Scotland declaring independence has sent cable into a tailspin, with sterling plunging 70 pips in thin trade, sliding below 1.24 on the news.
"Politics is not a game and I can't help but feel that the SNP does treat it as a game and they have this tunnel vision of only looking at the issue of independence".
The SNP accused May of hypocrisy, for criticising Scottish demands for independence while seeking a "hard Brexit".
The majority of Scots, 62 percent against 38 percent, voted to stay in the European Union at the 2016 nationwide referendum, however, the United Kingdom overall voted to leave.