On Friday, Trump said that at a gala dinner at Blenheim Palace the night before he and May spoke for nearly 90 minutes and had "probably never developed a better relationship".
The prime minister smiled and said there was "a lot to discuss", including "the special relationship, which is great, between the United Kingdom and US".
She said they would discuss "the real opportunities" on a USA trade deal, as well as foreign, defence and security issues "where we work really closely together".
Trump told the Sun newspaper he was avoiding the capital as much as possible.
The day also began with the highly anticipated Trump baby blimp being flown over Parliament square.
"I think he's got what it takes".
The president and first lady jetted to Scotland on Friday evening after talks with Theresa May and tea with the Queen at Windsor Castle, to Trump Turnberry on the west coast. It's an accurate representation of his politics which are so immature.
Mr Trump branded the Aberdeen bay windfarm his father had fought so hard to stop "irrelevant", but added that he was sceptical that it would still be standing in a decade. She wanted to go a different route ...
"What is interesting is Trump is not criticising mayors of those cities, but he is criticising me", he told BBC radio. "And that is fine", he said. "She's a total professional because when I saw her this morning, I said: "I want to apologize, because I said such good things about you". But it is too bad what is going on".
The government published its blueprint on Thursday calling for closer trade ties with the European Union after it leaves the bloc next March.
"I would have done it much differently", Trump said.
The Daily Telegraph stays with Brexit but tries to turn the attention back on the prime minister, with "Revealed: advice from Trump that May ignored". It was quickly followed by the resignation of two members of her Cabinet, Foreign Secretary Boris Johnson and Brexit Secretary David Davis, who did not approve of her approach.
"(Until) I remember her desperate rush to invite him, her repeated reluctance to criticise his Muslim ban or caging of children, her chasing him for a bad trade deal.
Mr Trump's visit came as watchdog Scottish Natural Heritage found the Trump International Links has "partially destroyed" the specially protected site it was built on.
Putin's government is accused by May's of unleashing a deadly nerve agent in the English city of Salisbury. It contrasts "the pomp" of Trump meeting the Queen, with the Labour leader's decision to join 100,000 protesters, calling him a "pygmy".
The president, whose mother was born in Scotland before immigrating to the US, will also be greeted by protesters, as several large demonstrations are planned in various Scottish cities.
Meanwhile, Mrs Trump played bowls with the PM's husband, Philip May, at the Royal Hospital Chelsea in London.
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