German newspaper Frankfurter Allgemeine Sonntagszeitung said the European Commission (EC) president walked out of Brexit talks in London last week saying he was "10 times more sceptical than before".
It led to a flurry of criticism of Ms May's Brexit negotiating strategy, with opposition parties warning the UK was heading for a "disastrous hard Brexit".
The reported disclosures were attributed to sources at the EC.
Ms May responded to the reports on Monday evening, repeating the line that the Downing Street meeting had been "constructive".
“I have to say from what I've seen of this account I think's its Brussels gossip - and just look at what the European Commission themselves said immediately after the dinner took place, which was that the talks had been constructive," she said.
According to the report, when the Prime Minister told them "Let us make Brexit a success", Mr Juncker replied "Brexit cannot be a success".
He then produced copies of Croatia's EU entry deal and Canada's free trade deal, which runs to 2,000 pages, to show how complex any future deal would be.
Ms May was also said to have angered the EU side when she warned that the UK could not be forced to pay a "divorce bill" for leaving because there was no requirement under the treaties.
As he left, Mr Juncker was said to have told her: "I leave Downing Street 10 times as sceptical as I was before."
No 10 earlier on Monday said it did not recognise the account of the meeting which took place over dinner last Wednesday.
A Government spokesman said: "As the Prime Minister and Jean-Claude Juncker made clear, this was a constructive meeting ahead of the negotiations formally getting under way."