Mr Barroso has been told by British politicians they now favour the euro
The government has denied a shift in policy on the euro after the European Commission's president said the UK was "closer than ever before" to joining.
Jose Manuel Barroso told French radio that British politicians were considering the move because of the effects of the global credit crunch.
Lord Mandelson said at the weekend that "our aim" should be to join the euro.
But Downing Street said its position on the single currency remained the same and that it had "no plans" to join.
"Our position hasn't changed... we have no plans to join the euro," No 10 said.
In 1997 Gordon Brown, seen as less keen on the euro than Tony Blair, set five economic tests which had to be met before ministers would recommend UK euro entry and holding a referendum.
The key test is whether the UK economy is coming together with those of countries in the eurozone and whether this can be sustained in the long-term. The second test, linked to this, is whether there is sufficient flexibility to cope with economic change.
The remaining three tests assess the impact of joining the euro on jobs, foreign investment and the financial services industry.
Opinion polls have suggested that any vote on scrapping the pound and adopting the euro would be lost, and in the UK the currency has not been a significant political issue for years.
In his interview Mr Barroso acknowledged "the majority" of British people continued to oppose joining the eurozone.
But he said the recent economic uncertainty had made the currency a far more attractive option.
In the RTL radio/LCI television broadcast, the former prime minister of Portugal said: "We are now closer than ever before.
"I'm not going to break the confidentiality of certain conversations, but some British politicians have already told me, 'If we had the euro, we would have been better off'."
He said the current poor economic situation had emphasised the importance of the euro to the UK, but added he believed a move would not take place in the immediate future.
"I know that the majority in Britain are still opposed, but there is a period of consideration under way and the people who matter in Britain are currently thinking about it," he said.
The value of sterling compared with other currencies has fallen during the credit crunch, and the UK government has had to spend massively in recent months to try to support the economy.
During the interview, Mr Barroso highlighted the situation in Denmark - an EU state which voted against joining the eurozone in 2000, but is now considering holding a new referendum on the single currency.
In the daily Brussels briefing later an EC spokesman said "member states would benefit from a country like Britain being in the euro".
He said the euro could be "an anchor of stability in troubled times... the advantages are very clear".
He added that Mr Barroso's comments were "reflections" and added: "The British are very pragmatic. When they feel it is right to join the euro, they will join the euro."
A Downing Street spokesman said: "We have no comment on this. Our position on the euro is the same. We have no plans to join the euro."
Business Secretary Lord Mandelson, a former European Commissioner, told Labour's Progress conference on Saturday: "I hold to the view that our aim, our goal, should be to enter the single currency."
He added that the government was "obviously not going to take on that challenge" in the current economic climate.
'Hunt them down'
The UK's opposition Conservative Party opposes adopting the euro.
Shadow foreign secretary William Hague said: "It is extraordinary that certain politicians are whispering to the EU Commission about joining the euro behind the British people's backs.
"Keeping the pound is vital for Britain's economic future. We need interest rates that are right for Britain, not the rest of Europe. There are no circumstances in which the next Conservative government will propose joining the euro.
"If Labour ministers still want to get Britain into the euro they should come out and say so. We will be putting questions to the government to find out what conversations have been going on."
The leader of the UK Independence Party, Nigel Farage, said "the people who matter in Britain are the people, not the professional political class that Barroso is himself a member of".
"That ruling elite would love to bounce us into the euro and will grasp at any straw to do so, for it's a step on the way to their dream and our nightmare, a federal superstate.
"We're told that some British politicians have said 'If we had the euro, we would have been better off'. Whoever these people are we need to hunt them down and explain some simple economics to them."
He added that if Mr Barroso wanted to test the mood in Britain "then he can call for a referendum on both the euro and the Lisbon Treaty so that the people of Britain can tell him where to go".