A Government spokesman said: "We would not comment on alleged remarks from a private conversation which is said to have been overheard in a hotel bar".
"Today the response of the Brexiteers is non, non, non et non".
But there remains a divide over the customs union, even though she did not reject any of his conditions outright.
Barnier told a news conference in Luxembourg that time was "extremely short" to conclude a deal before Britain is due to leave the bloc on March 29.
The best way to end uncertainty is to vote for a deal.
The UK economy grew by just 0.2% in the final quarter of 2018, down from 0.6% in the previous quarter, exceeding economic forecasts that predicted GDP growth would remain unchanged in the final three months of the year, according to data from the Office of National Statistics (ONS).
Britain is scheduled to leave the bloc on March 29. And seven of Britain's top 10 import markets are in the European Union, with Germany on top of the pile.
After talks in Strasbourg at the European Parliament, U.K. Brexit minister Stephen Barclay said there was "a lot of goodwill on both sides" to achieve a deal. It knows that there is a huge Remain majority in Westminster, that will do what it can to thwart Brexit.
Among the places with the most jobs at stake would be Wolfsburg in north-central Germany, where Volkswagen is headquartered, and the Dingolfing-Landau region in southern Bavaria, where BMW has manufacturing facilities.
The authors cautioned the figures do not predict that many people would be laid off.
Britain's economic slowdown should not be blamed entirely on Brexit, British Trade Minister Liam Fox said on Monday after data showed the economy previous year grew at its slowest since 2012.
United Kingdom trade secretary Liam Fox echoed the sentiment that the drops were not exclusively Brexit-related in Bern this morning after signing a trade continuity agreement with Switzerland: "Clearly there are those who believe that Brexit is the only economic factor applying to the United Kingdom economy".
But he rejected suggestions that the backstop arrangement - created to keep the Irish border open in the absence of a wider trade deal - was being treated as a "bridge" to a future UK/EU relationship, insisting instead that it is "an insurance policy that is never meant to be used".
"Brexit uncertainty is certainly not helping matters on the economic front, but it is probably only a secondary factor in this slowdown, with the primary cause being a drop in overall global activity", noted David Cheetham, chief market analyst at XTB trading group. It covers issues like free trade, public procurement, agriculture and the fight against fraud.
European Union leaders have turned down May's plea to renegotiate parts of the legally binding Brexit withdrawal bill, making the no-deal outcome more likely even though both sides believe it would harm their economies.
A Cabinet minister has insisted there is "no chance" of Theresa May accepting Labour's vision for Brexit despite speculation the Prime Minister could soften her stance on customs union membership.
Leading ERG member Mark Francois told the BBC: "We can not vote for this as it is now configured because it rules out no-deal and removes our negotiating leverage in Brussels".