German daily Frankfurter Allgemeine Zeitung (FAZ) said May "begged" Juncker for assistance, warning Europeans of the immense political risk she had taken domestically in backing away from a hard Brexit and asking for a two-year transition period.
The article, which did not cite sources, said May appeared "tortured," "fearful" and "discouraged" at a dinner with Juncker just days ahead of a summit in which EU leaders handed May a small victory by agreeing to start preparations for the next stage of negotiations.
The report which appeared on Sunday said Juncker later told colleagues that May appeared beaten down by party infighting and looked like she wasn't sleeping at night, with "dark circles" under her eyes.
A similar leak to the same newspaper after another private meeting between the pair in May ignited a diplomatic row. This time Juncker, his right-hand man Martin Selmayr and the European Commission's chief spokesman all lined up to issue speedy denials of the report.
Juncker told the BBC he was "shocked" by what appeared in the FAZ, insisting that "nothing is true" in it.
"It was a good meeting. She was neither tired nor defeated," Juncker later told a gathering of students in the French city of Strasbourg.
In a tweet, Juncker's cabinet chief Selmayr, who was at the dinner with May, also gave a staunch denial.
"I deny that 1/we leaked this; 2/Juncker ever said this; 3/we are punitive on Brexit," wrote Selmayr. "It's an attempt to frame EU side and to undermine."
Fraught atmosphere
Selmayr's response came after May's former joint chief of staff Nick Timothy took to Twitter to accuse him of leaking the information, calling it a "reminder that some in Brussels want no deal or a punitive one".
Selmayr, a former ECB official from Germany, is a powerful figure in Brussels, known as a skilled spin doctor and is often thought to be a source to FAZ, a conservative Frankfurt-based daily.
It is the latest leak to highlight the fraught atmosphere surrounding the talks, whose slow progress has stoked fears Britain could leave the European Union in March 2019 without a deal in place, risking economic and legal chaos.
The EU's Brexit negotiator Michel Barnier meanwhile said that the transition period could go up to 2020.
"At this stage I don't have a mandate on this point. But if we can reach an agreement, such a period that is short and clearly defined is possible," he told France's Les Echos financial newspaper. "It will give us a little more time to prepare the future relationship."
May is struggling to contain divisions within her government and Brexit hardliners have been quick to jump on any opportunity to paint Brussels as insincere or vindictive in their negotiating tactics.
Commission spokesman Margaritis Schinas accused unnamed people of trying to "point at us to serve their own political agendas, their own political priorities or even to undermine our negotiating position".
The row in May erupted after the FAZ reported that Juncker had left a dinner meeting with the British PM "10 times more sceptical" about the prospect of a Brexit deal and told German Chancellor Angela Merkel that May was in a "different galaxy".
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