May told the BBC on Sunday that is what Trump referred to in a Friday press conference when he said he had made a suggestion that May found "too brutal".
She said: "Interestingly, what the President also said at that press conference was "don't walk away, don't walk away from the negotiations because then you're stuck".
"We think it is possible to negotiate independent trade policies after we leave the European Union".
Meanwhile, Theresa May has warned Tory rebels seeking to wreck her blueprint to leave the European Union that they could be left with "no Brexit at all" unless they fall into line.
Davis, who quit as Brexit Secretary, used a Sunday Times article to accuse May of making an "astonishingly dishonest claim" that Brexiteers had not come up with an alternative to her plan.
Organizers said 250,000 people were protesting in London and other demonstrations were expected in cities around the country, including Windsor where the US President was due to have tea with Queen Elizabeth.
New MacBook Pro features debris-repelling keyboard, iFixit discovers
Apple on Thursday unveiled its 2018 MacBook Pro models , which are already available for purchase online and in Apple stores. Buried in the press release was a reference to a new keyboard, "an improved third-generation keyboard for quieter typing".
Speaking about the horrific terror attacks in London and Manchester, he said: "One of the comforting things for us were the words of love and support from those in America and I'm not sure why President Trump has singled me out as the Mayor of London". He added it was up to May how to handle Brexit, though he wants to ensure the U.S.
What do her critics say?
"The services sector is crucial for our economy and that's why it's really important that, the white paper... has no mention of what the Government's plans are to protect that very important sector".
Since setting out the five tests for a Brexit deal in her Mansion House speech, Mrs May had been "in a headlong retreat but in an oddly secretive manner", Mr Rees-Mogg said.
After hours of talks at her Chequers country residence she appeared to have won over her cabinet, but just two days later David Davis resigned as Brexit secretary, followed by her foreign minister, Boris Johnson, the next day.
He described her as a "Remainer who has remained a Remainer".
"An establishment elite who never accepted the fundamental right of the public to choose democratically their institutions are working towards overturning them".