"Michel Barnier and his taskforce can not negotiate an outcome that compromises the integrity of the single market for everybody else".
The UK Government says such a solution would tick two boxes: It would avoid the need for a hard border between Northern Ireland and Ireland; and without harming the internal market of the UK - "doing so in a way that fully respects the integrity of the EU's single market, customs union, and its rules-based framework".
The comments, following on from the morning press conference, will be a cause of great concern for Mrs May.
Trump's interview with British tabloid The Sun was published on the same day he arrived in London, shortly after May revealed plans for a still semi-cozy working relationship between the United Kingdom and the European Union even after Brexit is finalized.
He told The Sun Mrs May's plan would affect trade "unfortunately in a negative way".
May has previously said she does not believe her Brexit plans should rule out a trade deal with the United States.
"I would say Brexit is Brexit", Mr Trump said on Thursday at a news conference at the North Atlantic Treaty Organisation summit in Brussels.
While Trump's trip was not the full state visit he was originally promised, he was heralded by military bands on his arrival in the country and at Blenheim, and he is scheduled to have tea with Queen Elizabeth. I get along with her very nicely.
As he began a four-day visit to Britain on Thursday, Trump, a major supporter of Brexit, told The Sun that he had advised May to go about leaving the European Union in a different way but was ignored. She praised the friendship between the two allies, glossing over Trump's previous remarks that Britain was a "hot spot" in turmoil over Brexit.More news: MLB All-Star Game rosters feature the game's biggest stars
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"I am not pitting one against the other".
"I think he has done a bad job on crime, if you look, all of the awful things going on there, with all of the crime that is being brought in", Trump said of Khan.
The Trumps landed at Stansted Airport, Essex, at 13:50 BST before a helicopter took them to Winfield House in Regent's Park, where they are staying as guests of the USA ambassador.
It also confirms that Brexit will take place on 29 March 2019.
Demonstrators lined the streets outside Blenheim Palace in Oxfordshire where the President and First Lady attended the black-tie dinner.
Some carried placards saying Special Relationship?
They were given a best-of-British dinner, featuring Scottish salmon, Hereford beef fillet and strawberries with clotted cream ice-cream.
The open attack on his host during a visit expected to be marked by loud as massive protests was likely to cast a heavy shadow over a planned Friday meeting between Trump and May in London, further chilling an already frosty relationship.
Demonstrators are also gathered outside the USA ambassador's residence in London, where the Trumps are staying for Thursday night.
Incoming Brexit minister Dominic Raab described the proposal as "innovative" and said it is now up to the European Union to respond "in kind".
Just hours before Trump's interview was published, May invoked Winston Churchill, a hero of Trump, as she addressed the U.S. president and business leaders at a black-tie dinner at Blenheim Palace, the grand 18th-century country house that was the birthplace of the British World War Two leader.