"He told me I should sue the European Union - sue the European Union, not go into negotiations", she said.
However, Mrs May continued to insist a deal was possible during a press conference with the President the next day - when he suggested she could take a different approach to negotiations with the EU.
In an article with the Mail on Sunday, May urged her critics in the Conservative party to rally behind her proposal and vowed not to compromise national interests during negotiations in Brussels.
This way, the trade between the member states is carried out freely without much restraints and customs checks, but they can not strike their own deal with other nations outside the EU.
A White Paper published on Thursday fleshed out details of her plan, which advocates close links with the European Union on trade in goods, but not services.
May is battling for her political survival after announcing a negotiating plan that infuriated factions on both sides of her Conservative Party: eurosceptics say the plan leaves Britain too close to the European Union, while pro-European lawmakers say it leaves the country too distant.
He told Good Morning Britain: 'I think we're going to have a great trade deal.
They believe that would leave the United Kingdom as a "rule-taker" from Brussels, and could thwart future trade deals with countries including the USA.
May has previously said that she does not believe her Brexit plans should rule out a trade deal with the United States.
He described her as a "Remainer who has remained a Remainer".
"We need to keep our eyes on the prize". "If we don't, we risk ending up with no Brexit at all".
In an interview published by The Sun, Trump said May's plan for the Brexit was counter to what "Leave" supporters approved in a referendum in 2016.
"I'm happy to sit down and listen and hear concerns from my colleagues", the prime minister told lawmakers.
After two years of government squabbling and parliamentary rifts on Brexit, support is growing for the idea that only another referendum can resolve Britain's future outside the EU.
However, the danger to the Prime Minister was underlined by the disclosure that Brexiteers had set up a Whatsapp group to co-ordinate voting tactics, organised by ex-Brexit minister Steve Baker, who quit over the Chequers plan.
Former education secretary Justine Greening today called for a second referendum, labelling Theresa May's recent Brexit deal a "fudge".
Ahead of a crucial week in Parliament, the Prime Minister acknowledged feelings in the party were running high, but said her plan offered a "hard-headed and practical" way forward.
Ms May added that if party members called for a leadership spill she would stand in the contest, claiming that she is in it for the long term.