Trump will end his day with a trip to his Turnberry golf club course in Scotland.
One of the organisers behind "Baby Trump", Kevin Smith, said it was devised by a group of friends who got together in a pub.
Trump has sided firmly with Brexiteers, saying what May proposed would hurt the chances of a future trade deal between the United Kingdom and the US.
Trump's interview with the paper came after his contentious meeting with North Atlantic Treaty Organisation members in Brussels and ahead of his scheduled visit with Queen Elizabeth II.
Last week at the same location, May finally won agreement for her Brexit plans from her cabinet but within days two senior ministers had quit, departures which Trump said earlier in the week had left Britain in turmoil. And he seems to do very well - I was just with him tonight, and I saw him with the Prime Minister sitting there. But I'm different than other people.
Prince Harry Jokingly Scolds Toddler for Touching Meghan Markle's Hair
Traditionally, members of the royal family are supposed to refrain from showing any political views and are not allowed to vote. It's an interesting choice for the mother-to-be, who in the recent weeks has flaunted her growing bump in chic maternity wear.
The president said May is "doing a fantastic job" as British prime minister and said "I think she's a terrific woman". "As he said in his interview with the Sun she "is a very good person" and he 'never said anything bad about her, '" White House Press Secretary Sarah Sanders said. "If the strategy at North Atlantic Treaty Organisation was to shore up more spending in some ways, the president didn't want to take the win that he had because actually North Atlantic Treaty Organisation allies have been increasing spending on their own defense, which they haven't yet hit the deadline for in 2024. And I said to him, 'This special relationship is better than ever, ' and he said, 'It is.' I could see the chemistry between them was very good", Ruddy said.
But older voters who voted for Brexit in far greater numbers than their juniors, were much more likely to say Mr Trump could be trusted: 51% of people aged 55 and over consider Mr Trump trustworthy, while 62% of 18-34s think he is not to be trusted.
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London", Trump told the newspaper.
"I used to love London as a city", Trump said. I haven't been there in a long time. "I think you're losing your culture".
Trump spoke out against the balloon and against London mayor Sadiq Khan, who approved its launch.
Khan in the past has publicly feuded with Trump after the president criticized him over the city's response to a terror attack. "Relationship is very important".
The president, however, did not back down from the controversial comments he made about immigration in the Sun interview, calling the influx of migrants a "very negative thing for Europe" during Friday's remarks.