A spokeswoman for European Commission president Jean-Claude Juncker said the leaders of the remaining 27 countries “have been very clear” that what is on the table “will not be renegotiated”.
Mrs May is trying to get concessions on plans for the Northern Irish backstop in the hope it will convince MPs to vote her deal through Parliament later this month.
At a press conference in Brussels this morning, Mina Andreeva, deputy chief spokeswoman for the European Commission, was asked what talks will be held before the Commons has its say on the deal on the week of January 14.
She said: “No further meetings are foreseen between the commission’s negotiators and the UK negotiators as the negotiations have indeed been concluded.”
“We have said many times the deal that is on the table is the best and only deal possible… the EU27 leaders confirmed on December 13 in their conclusions that it will not be renegotiated,” she added.
She said Mr Juncker is “always willing to listen Mrs May’s views on the backstop” but, when asked what he can do to help get her deal through Parliament, she rebuffed any chance of altering the backstop as it stands.
Ms Andreeva said: “Our solutions are on the table, we are ready to listen but… the EU 27 leaders have been very clear that it will not be renegotiated, what is on the table.”
She said that, in a newspaper interview at the end of December, President Juncker “reiterated very clearly that now it is up the British people and MPs to decide on the next steps”.
She added that the EU side has “started the ratification process” on the terms in the withdrawal agreement.
Her words come after the Brexit Secretary warned that no-deal will be “far more likely if MPs reject the Government’s Brexit deal later this month”.
Writing in the Daily Express, Stephen Barclay said: “There is obviously division in Parliament over the PM’s Brexit deal. It’s not a perfect deal.
“But it’s the only workable deal that delivers on the democratic choice of the British people. And it’s the best way to avoid no-deal. As we return to Parliament, MPs must consider the alternative.”
The cabinet minister also confirmed the government is to “accelerate our no-deal planning further”, adding: “The pace and intensity of the work we are doing reflects the potential scale of this disruption to people and businesses across the UK that a no-deal scenario could bring.”
He added: “And, on Tuesday, we will start a new phase in our public information campaign, using radio and social media to further raise awareness about the need to prepare.”