Her ex-adviser Nick Timothy accused EU official Martin Selmayr of being the source of an account in a German paper claiming Mrs May was politically weak and had "begged for help" at a dinner.
He claimed it showed "some in Brussels want no deal or a punitive one".
Mr Selmayr denied involvement and said it was an attempt to "frame" the EU.
He is a senior aide to European Commission President Jean-Claude Juncker, who had the dinner with Mrs May in Brussels last week ahead of an EU summit.
The apparent leak of what happened in the dinner follows a similar incident in April, when Mrs May accused some in the EU of "meddling" in the general election campaign after details of a dinner between her and Mr Juncker in Downing Street appeared in the German press.
Downing Street said it had no comment on the latest reports and pointed out that both sides were of the view that the recent get-together had been "constructive and friendly".
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And Foreign Secretary Boris Johnson said that although the tone of last week's summit was "more positive" than he expected, he wanted the EU to "get on" with talks on trade.
Meanwhile, five leading business groups have joined forces to call for a swift agreement on a transitional deal in which firms can operate largely on the same basis as now.
Later on Monday - from about 15:30 BST - the prime minister will report back to Parliament on the outcome of last week's summit.
At that gathering the other 27 EU leaders decided progress on the Brexit separation issues had not been "sufficient" to open talks on future trade relations with the UK yet - but they did agree to discuss the issue amongst themselves, paving the way for talks to possibly begin in December.
Before returning to the UK, Mrs May said there was "some way to go" but added that she was "optimistic".
She has been under growing pressure at home with some Conservative MPs urging her to walk away from the talks if trade discussions do not begin soon, while Labour has warned of the increasing risk of leaving without a deal.
On Sunday, German newspaper Frankfurter Allgemeine published an unsourced account of a dinner on Thursday at which Mrs May addressed EU leaders, after which both sides agreed to accelerate talks.
The account, largely written from the perspective of EU officials, suggested Mrs May appeared "anxious, despondent and disheartened" and had spoken of her limited room for manoeuvre back at home.
"Everyone can see: the prime minister is marked by the struggle with her own party," the article stated, according to a translated version quoted by a number of British newspapers.
"She has deep rings under her eyes. She looks like someone who doesn't sleep at night."
'Fair wind'
Mr Timothy, who was the PM's chief of staff until he quit after the general election, suggested the disclosure had all the hallmarks of coming from the European Commission.
He tweeted: "After constructive Council meeting, Selmayr does this. Reminder that some in Brussels want no deal or a punitive one."
But Mr Selmayr said the claim was "false" and neither he nor Mr Juncker had any "interest in weakening" Mrs May.
He tweeted: "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."
The European Commission said it was working for a fair Brexit deal and had "no time for gossip".
"Some people like to point at us to serve their own political priorities," a spokesman said. "We would appreciate if these people would leave us alone."
Conservative MP Crispin Blunt, a former chair of the Commons foreign affairs committee, said the account was "impressionistic" and he did not think anyone would take it "too seriously".
International Development Secretary Priti Patel described it as "commentary at the margins" and said Mrs May was "fighting for the best deal" for the country.
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