Scottish Secretary David Mundell said he "dreads" a second Scottish independence referendum but does not believe Scotland would vote to leave the UK.
He said another vote on the issue would be "seriously unpleasant and divisive" and set "Scot against Scot".
Mr Mundell refused to clarify whether the UK Government would block moves for a second referendum in light of the Defence Secretary Michael Fallon's indication earlier this week that Westminster would not grant permission.
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The Scottish Secretary has previously said the UK Government would not frustrate attempts for a further referendum on Scottish independence but pressed on this issue on the BBC's Sunday Politics Scotland show he said it was not an issue as there is currently no proposal on the table.
First Minister Nicola Sturgeon has agreed a second referendum is "all but inevitable" following Prime Minister Theresa May's plans for a hard Brexit removing the UK from membership of the single market.
Mr Mundell said: "Of course there could be another referendum, that is a process issue. But the people of Scotland are very clear that they don't want one and that's what we need to continue to debate about."
He added: "I'm not feart of another referendum, as Nicola Sturgeon likes to suggest, because I think it is pretty clear the outcome would be the same.
"But I dread it because I think it would be a divisive and seriously unpleasant event which would set Scot against Scot and I don't think people want to see that."
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He also said the Scottish Government's proposal to remain part of the single market through the European Free Trade Agreement as well as staying in the UK was "not impossible".
He said : "It's not impossible but I believe that it's better to proceed on the basis that the Prime Minister set out of getting access to the single market for the whole of the United Kingdom with a free trade agreement.
"I don't see the evidence to suggest that Scotland needs or would benefit from a differentiated agreement but my mind is open and we've intensified discussions to look at that."
Scotland's Brexit minister Michael Russell said: "David Mundell's forced admission that it is possible for Scotland to remain in the United Kingdom and the European single market is a significant concession from the Tories.
"The people of Scotland did not vote for Brexit and David Mundell is alone as the only one of the nation's 59 MPs who backed the UK Government by voting to trigger Article 50 - despite the grave consequences."
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The SNP minister went on: "David Mundell twisted and turned when repeatedly asked if he would block an independence referendum but the Tory leadership must realise that it is the people of Scotland, not them, who have the right to choose.
"Without that option, Scotland would have to accept whatever decisions the UK Government makes - no matter how reckless and damaging they are to Scotland's interests."
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