Speaking at the North Atlantic Treaty Organisation summit in Brussels before he arrived, Mr Trump said the United Kingdom was a "hot spot right now".
Trump personally criticized May's handling of Brexit, saying that her so-called soft-Brexit approach went "the opposite way" to what he had recommended and that it was "very unfortunate".
Trump has clashed in the past with May - even though she is a conservative who shares his view that defense spending should be raised - and with her predecessor, David Cameron, who challenged Trump's anti-Muslim campaign stance as "divisive, stupid and wrong".
"The idea that you can blame this on immigration from Africa is I think preposterous and we should call him out when he does so", Khan told BBC radio on Friday.
In a statement ahead of Trump's arrival, she said the visit would focus on trade and strengthening defense and security ties, saying there was no stronger alliance than Britain's "special relationship with the U.S".
"We have enough difficulty with the European Union", he said.
"Once we have our agreement with the European Union in place, I'm confident that there will be the latitude and the ability to do a significant trade deal with the United States".
In another blow to May, Trump said her now ex-foreign secretary "would be a great prime minister".
Trump's remarks came as he prepared to meet May for a working lunch at Chequers.
Liverpool agree £13.75m deal for Stoke star Xherdan Shaqiri
Adding the Switzerland worldwide can provide much-needed cover for star forward Mohamed Salah in particular. Shaqiri is believed to be keen on a move to Anfield but could be offered the chance to return to Italy.
The interview posted online as Prime Minister May welcomed President Trump and the first lady at Blenheim Palace for a lavish gala dinner.
Some signs at Thursday's protests condemned Trump's immigration policy, demonstrating the worldwide outrage he has drawn for separating families at the U.S. -Mexico border and imprisoning children and babies away from their parents.
Trump said, however, that he "feels unwelcome" in London due to the thousands of people expected to protest in the British capital, as well as other cities. "He obviously likes me, and says very good things about me", Trump said.
"Boris Johnson's a friend of mine, he's been very nice to me, very supportive and maybe I'll speak to him when I get over there".
Just hours earlier at a lavish dinner to mark Trump's first visit to Britain as president, May made a direct pitch for a deal with Washington.
While the White House had previously denied the president's schedule in London was meant to keep him away from the protests, Trump admitted as much in an interview with the British-owned tabloid "The Sun".
May and Trump are scheduled to hold talks and a joint news conference on Friday.
In one tweet on Thursday, Khan didn't mention Trump by name - but said Londoners have the moral duty to protest when shared US-UK values are under attack.
They will then meet the Queen for the first time, at Windsor Castle, before heading to Scotland where the USA president will spend the weekend at his Turnberry golf course in Ayrshire.