Senior Tory Chris Grayling has predicted Labour is in danger of not winning a single constituency seat in the Holyrood election.
The leader of the House of Commons said he was confident the Scottish Tories would.
He admitted it would be a “stretch” for his party to overtake Labour overall, however, adding it would be an “extraordinary blow” if it did.
Mr Grayling also warned those in favour of an independent Scotland should “take a step back”.
And he said in view of the low oil price a second referendum anytime soon was “utterly financially unrealistic”.
Former UK Justice Secretary Mr Grayling told the Press and Journal he was optimistic about the Scottish Conservatives’ chances in May.
The Epsom and Ewell MP added: “I think what’s going to be very interesting is that I think there is a real question mark as to whether Labour will win any constituencies at all in Scotland.
“Whereas I’m pretty confident we will win some constituencies in Scotland. It’s clearly a battle between us and Labour to come second.
“If we actually overtake Labour that would be an extraordinary blow.
“I think it’s a stretch but we are working towards it.
“I don’t think Labour will win a single constituency or they are in danger of not winning a single constituency.
“That really would be a desperate reversal for them.”
At a Press Gallery event in Westminster, he was also asked whether he believed the SNP was bluffing by threatening a second independence referendum in the event the UK votes to leave the EU, but Scotland votes to stay.
The Eurosceptic Cabinet minister replied: “I think they are making a noise but I don’t think they are actually really intending to try for a second referendum.
“With the collapse of the oil price, if Scotland had voted for independence it would now be in deep trouble financially.
“They would have the most monumental financial black hole.
“The idea Scotland could now suddenly have in whatever circumstances a second referendum and vote for independence any time soon I think is just utterly financially unrealistic.
“I think anyone in Scotland who is thinking about independence should take a step back.”
In response, the SNP’s Angus MacNeil said the latest opinion poll showed 54% of Scots would support a second referendum under those circumstances.
The Western Isles MP also pointed to the Irish economy which he said had no oil, yet grew 7% this year.