The unnamed minister is said to have claimed such a union would "of course" be negotiated, possibly in exchange for retaining the UK's nuclear submarine fleet on the Clyde.
The comments provoked a furious row last night as Deputy First Minister Nicola Sturgeon insisted the No campaign's "supposed trump card" had been demolished.
The UK Government immediately disowned the statement and repeated George Osborne's original warning that a currency union between the countries would not happen in the event of a Yes vote on September 18.
Under its plans for independence, the SNP wants Scotland to share the pound with the rest of the UK as part of a euro-style sterling zone.
But Mr Osborne, backed by his opposite numbers from the other main Westminster parties, ruled out the proposal as too risky, in a move No campaigners hoped would deal a hammer blow to the First Minister's case.
However, last night a newspaper reported a UK minister as saying: "Of course there would be a currency union. There would be a highly complex set of negotiations after a Yes vote with many moving pieces. The UK wants to keep Trident nuclear weapons at Faslane and the Scottish Government wants a currency union - you can see the outlines of a deal."
The comments were dismissed by Scottish Secretary Alistair Carmichael. He said: "An anonymous, off-the-record quote does not change the stark reality on the currency. The UK Government has listened to the views of the Governor of the Bank of England and the independent advice of the Permanent Secretary to the Treasury that a currency union would be damaging for all the United Kingdom.
"That's why a currency union simply will not happen. The Scottish Government should remove the uncertainty on the currency by coming forward with a Plan B."
Deputy First Minister Nicola Sturgeon said: "This was supposed to be the No campaign's trump card, but as the polls show it has backfired badly - the gap between Yes and No has halved since November, and most Scots simply do not believe the bluff and bluster we had from George Osborne, Ed Balls and Danny Alexander.
"Now that the card has been withdrawn, it gives an even bigger boost to the Yes campaign. And it can only add to the sense of crisis which is engulfing the No campaign."
Recent polls from ICM and YouGov have shown the Yes campaign closing the gap despite a number of major companies voicing concerns about the impact of independence.
In a particularly painful blow for the No camp, the YouGov poll also showed 45% of voters thought Mr Osborne was bluffing when he ruled out the proposal for a formal pound-sharing deal.
Better Together yesterday stressed it would continue to pose "difficult questions" about Alex Salmond's plans for independence, rebutting claims it was about to drop "negative" warnings about the consequences of independence from a forthcoming advertising campaign and instead focus on positive messages.
The row came after Scottish LibDem leader Willie Rennie warned a Yes vote had become a "distinct possibility" and damaging tensions within the pro-UK Better Together campaign surfaced when a senior LibDem MSP publicly criticised Labour's performance in the referendum battle.
Tavish Scott, a former leader of the Scottish Liberal Democrats, said Labour allies in the Better Together group were not doing enough to win No votes in the party's traditional Central Scotland heartlands.
He also claimed Alistair Darling, the former Labour chancellor who heads Better Together, was not the best person to reach out to such voters.
Mr Scott spoke out during a fringe meeting at the Scottish LibDem conference in Aberdeen yesterday. His comments piled more pressure on Better Together just hours after campaign chiefs were forced to dismiss reports they were refocusing a major advertising drive to project a more "positive" message.
The claims followed two polls in recent days showing the No side's lead shrinking, as voters apparently rejected a succession of warnings about the economic prospects of an independent Scotland.
Discussing the pro-UK campaign, Mr Scott said the current crop of Labour politicians were relatively unknown compared with former MPs such as John Reid and George Robertson.
He said "former stars" should be used to target traditional Labour voters and added: "I don't think Alistair Darling is pulling that whole swathe of people back into definitely voting for the Union. What Alistair does is make an intellectual case, which he does very well, but that's a different sub-set of the electorate."
In a direct blast at Labour's efforts, he said: "Surely by now they would have realised it's their vote that's the crucial one. Our voters will vote No, Tory voters will vote No, the folk who matter more than anyone else is this group in the middle - Labour voters. They're the ones we need to get hold of."
Scots Labour leader Johann Lamont is attempting to position her party firmly to the left of the SNP. A party spokesman said: "Labour's positive case for Scotland staying strong in the United Kingdom is relevant all over the country. We will continue to have a range of voices delivering that message."
A Better Together spokesman said: "We agree with Tavish Scott. Everyone who believes that we are better and stronger as part of the United Kingdom has to get involved with the campaign to ensure we win in September."