German newspaper FAZ reported after the meeting that Juncker had told colleagues how May "seemed anxious...despondent and discouraged."
The unnamed sources painted a picture of May as “tormented...sleep-deprived, with deep rings beneath her eyes."
Juncker denied the account and dismissed allegations that his office leaked the details, telling the BBC : "Nothing is true in all of this. I had an excellent working dinner with Theresa May. She was in good shape, she was not tired, she was fighting as is her duty so everything for me was ok."
Asked whether she had "pleaded" with him over getting Brexit progress, he added: "No, that's not the style of British prime ministers."
Martin Selmayr, Juncker's abrasive chief of staff, has also denied being involved in the leak.
After being accused by former Number 10 aide Nick Timothy, he tweeted this morning: "This is false. I know it doesn't fit your cliché, but Juncker & I have no interest in weakening PM."
He added: "I deny that 1/we leaked this; 2/Juncker ever said this; 3/we are punitive on Brexit. It's an attempt 2 frame EU side & 2 undermine talks."
But not everyone believed his denial. Dan Korski, Downing Street's deputy head of policy under David Cameron, tweeted that Selmayr "isn't representative of broader EU but of the worst federalist dreams".
"He leaks 2 keep the fantasy alive," Korski added.
A Downing Street spokesman declined to comment on the row, pointing instead to the joint statement both sides released shortly after the meeting, which characterised the dinner as "constructive and friendly."