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 last Wednesday 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 German newspaper's report of the dinner, 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 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 No 10 spokesman said the UK was approaching the talks constructively and in a spirit of goodwill towards the EU, but was also determined to make a success of leaving.
In a speech later on Tuesday, Mrs May will suggest the two-year Brexit process will be tough and the other 27 nations are "united in their determination to do a deal that works for them."
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."