Trump's suggestion that her Brexit plan will kill any such deal has given her opponents ammunition against her, and could potentially spark a chain of events that leads to her downfall.
Speaking to reporters in Belgium after a fiery Nato Summit, Mr Trump had described the United Kingdom as a "hot spot right now with a lot of resignations" and dismissed the Prime Minister's Chequers plan on the next stage of Brexit.
Many in the pro-Brexit camp say Britain should seek a trade deal with the U.S.at the earliest opportunity.
US President Donald Trump (C) gestures as he poses alongside Britain's Prime Minister Theresa May (2R) and Iceland's Prime Minister Katrín Jakobsdóttir (R) during the opening ceremony of the NATO (North Atlantic Treaty Organization) summit, at the NATO headquarters in Brussels, on July 11, 2018.
"I told her how to do it. I think he's got what it takes".
In an interview with Britain's Sun newspaper published late on Thursday, Trump said May's plans for a business-friendly Brexit would leave it too close to the European Union to allow a new trans-Atlantic trade deal to be struck.
He added: "I've been reading a lot about Brexit over the last couple of days and it seems to be turning a little bit differently, where they're getting at least partially involved back with the European Union".
Earlier, British Prime Minister Theresa May invoked wartime leader Winston Churchill and strong transatlantic ties as she hosted Trump Thursday night - hours after he began a protest-laden visit by questioning her Brexit strategy.
On Friday, he will hold talks with May expected to focus on Brexit and Russian Federation, at the prime minister's Chequers country residence followed by a press conference.
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London", Trump said in an interview published today.
Mr Trump will touch down for his highly controversial four-day trip which has sparked protests and demonstrations in the capital leaving taxpayers footing a police and security bill of up to £10 million.
A high fence has been erected around the USA ambassador's central London residence where Trump will spend Thursday night and the embassy has sent out an alert warning Americans in London to keep a low profile in case protests turn violent. Vince Cable, the leader of the pro-EU Liberal Democrats, said, "Most of us don't think he is particularly good judge on Brexit or anything else".
"Now he might not like the current president, but I represent the United States", Trump said.
Trump's schedule will largely keep him out of central London, however. "I think he is a great representative for your country".
And then there's the royal moment that the world will be watching on Friday: the moment that Trump meets the Queen.
Trump will later Friday take tea with Queen Elizabeth II at Windsor Castle, before spending the weekend in Scotland on a private visit that will likely take in 18 holes at one of the property magnate's golf courses, where more protesters await him.