The comments will plunge the transatlantic "special relationship" to new lows, making for extremely awkward talks with May when the two meet at her country retreat of Chequers later on Friday.
Trump's visit to Britain followed two days of a North Atlantic Treaty Organisation summit in Belgium, where the US president shook up the conference with rhetoric about other members failing to meet fiscal defense requirements, the possibility that he could end the United States' 70-year membership in the alliance and Germany being "captive" to Russian energy.
And the Mayor of London also defended allowing a giant balloon depicting Mr Trump as an angry baby to fly near Parliament.
"There is no stronger alliance than that of our special relationship with the USA and there will be no alliance more important in the years ahead", May said in a statement.
Looking ahead to his meeting with Russian president Vladimir Putin on Monday, Trump said he would be discussing many topics but his biggest hope was an agreement to substantially reduce nuclear proliferation - his ultimate dream was to get rid of the weapons altogether, he said.
Donald Trump has heaped praise on "incredible" Theresa May and hailed UK-US relations as the "highest level of special" hours after incendiary comments criticising her premiership.
Sheila Menon, one of the organizers of the balloon, told CNBC's Steve Sedgwick that this protest has become so popular because "so many people have a very strong opinion about President Trump".
"As he said in his interview with the Sun she "is a very good person" and he 'never said anything bad about her.' He thought she was great on North Atlantic Treaty Organisation today and is a really terrific person", Sanders wrote.
Trump also spoke on immigration policy in the interview, saying that Europe was losing its identity and culture because of an influx of migrants.
"Fortunately, we tend to record stories now so we have it for your enjoyment if you'd like it", he said.
"When Trump visits the United Kingdom on Friday the 13th of July this year, we want to make sure he knows that all of Britain is looking ... and laughing at him", the campaign page said. It was one of more than a hundred protests police expected during Trump's four-day trip.
But well away from the noisy demonstrations, Mr Trump and Mrs May took questions from reporters.
Trump then heads to Windsor Castle later Friday for tea with Queen Elizabeth II. "Right now we're going to be talking about some things taking place in the Middle East and elsewhere".
"I think it changed the fabric of Europe and, unless you act very quickly, it's never going to be what it was and I don't mean that in a positive way", he said.
And, although he insisted he was not trying to pit Johnson against May, he added: "I am just saying I think he would be a great prime minister".