It follows reports in a German paper of repeated clashes between Theresa May and Commission president Jean-Claude Juncker at a Downing Street dinner.
EU sources claimed UK misunderstanding of the talks process, and ignorance about how Brussels works, could lead to no deal being agreed on the UK's exit.
Home Secretary Amber Rudd said the reports were "tittle-tattle".
She said the emergence of the reports was "not the right way" of negotiating, but the UK was committed to negotiating in "good faith".
According to the Frankfurter Allgemeine, the prime minister and Mr Juncker reportedly clashed over Mrs May's desire to make Brexit "a success" and whether the issue of protecting the rights of expat UK and EU nationals could be agreed as early as June.
The newspaper claimed Mr Juncker said: "I leave... 10 times more sceptical than I was before."
In a speech later on Tuesday, Mrs May - who has dismissed the account as "Brussels gossip" - will cite the need to stand up to the other 27 EU countries
"We have seen in recent days, it will not be easy," she will say. "The negotiations ahead will be tough. Across the table from us sit 27 European member states who are united in their determination to do a deal that works for them."
The German newspaper's report of the dinner last Wednesday, which looks to have come via European Commission sources, said that after the PM said she wanted to "make Brexit a success", Mr Juncker's response was: "Brexit cannot be a success. The more I hear, the more sceptical I become."
And when she said the UK owes no money to the EU, the president informed her that she was not leaving a "golf club".
The article said that, after last week's dinner, Mr Juncker was shocked at Mrs May's suggestion that a deal on citizens' rights could be achieved so quickly.
The German newspaper report also suggested Mr Juncker said there would be no trade deal between the UK and the rest of the EU if the UK failed to pay the "divorce" bill which it is expected to be asked for.
Reports also claim that the morning after the dinner last Wednesday Mr Juncker told German chancellor Angela Merkel that Mrs May was "on a different galaxy".
A senior Conservative source told the BBC that the party would "rise above" all the media coverage but rejected accounts of the dinner, saying: "We really, really do not recognise those reports."
Ms Rudd said the UK would not be responding to the claims but the government had set out a clear plan and priorities for the talks and Mrs May was the best person to negotiate a Brexit deal that was in the UK's "national interest".
"Once you start engaging in gossip, in tittle-tattle in this way, it (will) carry on and who knows where it will lead?" she told BBC Breakfast.
"Nobody knows how much truth there is in gossip. But there are ways of conveying what is going on and this is not the right way.
"I do not recognise the tone in which this has been reported but I come back to the fact that it does make it clear that it is going to be a complex, potentially difficult negotiation at times and who do we want leading those - we want Theresa May leading them, not Jeremy Corbyn."
Welcome to the EU/UK dominated Brexit Galaxy of Spin and Counter-Spin. A crazy old place. The galactic atmosphere is such these days that the dimensions of truth are elastic; at times, distorted.
Take the arguments this weekend over whether the Downing Street dinner last Wednesday at which Theresa May hosted European Commission President Jean Claude Juncker was a complete disaster or not.
Not at all, insists Downing Street.
But according to an EU diplomat, speaking to Germany's Frankfurter Allgemeine Zeitung and thereafter hitting Twitter and headlines across the UK, they went "badly, really badly".
He reportedly went as far as to say the British government was now "living in a different galaxy" to the EU when it came to Brexit expectations. This all seems rather inflammatory, so who's right and who's stretching the truth?
The accounts of the dinner were seized upon by European politicians and opposition parties in the UK.
Guy Verhofstadt, the former Belgian prime minister who leads the Alliance of Liberals and Democrats for Europe, said it was time to "get real". He tweeted: "Any Brexit deal requires a strong and stable understanding of the complex issues involved."
Former Lib Dem leader Nick Clegg said Theresa May's desire to pull the UK out of the single market and other EU institutions was leading to an "increasingly belligerent" atmosphere with the EU.
"No 10 appears to be treating the rest of the EU as if they are running the Home Office, just barking instructions and expecting them to fall into line," he told BBC Radio 4's Today
"This is a complex, Rubik's Cube negotiation which requires agility and charm to be successful. None of that appears to have been in evidence at that dinner last week."
Labour leader Jeremy Corbyn said Mrs May was sending out "rather mixed messages".
"To start negotiations by threatening to walk away with no deal and set up a low tax economy on the shores of Europe is not a very sensible way of approaching people with whom half of our trade is done at the present time."
However, UKIP leader Paul Nuttall urged Mrs May not to give any ground, tweeting: "We don't owe the EU a penny and in fact there is a pretty good case that they owe us."
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The UK will not enter into "a briefing war" with the European Commission over Brexit talks, Tory sources have said.