German daily Frankfurter Allgemeine Zeitung (FAZ) said that May "begged" Juncker for help in the negotiations, 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 an EU summit in which EU leaders handed May a small victory by agreeing to start preparations for the next stage of negotiations.
In a tweet, Juncker's cabinet chief Martin Selmayr, who also attended the dinner with May, staunchly denied the newspaper report.
"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."
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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".
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.
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 negotiatiing position".
A diplomatic row had erupted in May following a similar report in the daily 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".
That report was widely attributed to Selmayr and came just weeks ahead of British elections that turned into an embarrassing debacle for May who lost her majority in the UK parliament.