He added that Europe as a whole was "losing its culture" because of immigration from the Middle East and Africa.
There are street protests of Trump's first visit to Britain since taking office almost 18 months ago.
At Chequers, Trump and May will discuss foreign policy, according to White House officials.
"The president likes and respects Prime Minister May very much", she said. It is not considered appropriate to call the Queen by her first name - a gaffe that Nelson Mandela made in 2014 - and it is never okay for people to use her nickname Lilibet, which is reserved exclusively for very close family members.
Trump's interview easily could overshadow the government's attempt to lay out plans for what it calls a "principled and pragmatic" Brexit.
His departure from the USA ambassador's residence aboard the presidential helicopter was met by jeers from demonstrators banging pots and pans, and another group of protesters lined roads near the palace.
"The relationship is very strong", Trump insisted, though he did not directly answer questions about the Sun interview.
"If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal", he told The Sun.More news: China-made medicines with Valsartan to be withdrawn
The interview appeared in The Sun, Britain's biggest-selling newspaper, and was published shortly after May delivered a speech to welcome the U.S. president to Britain.
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London", he said.
The president told The Sun: "If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal".
Despite their daily differences, even the British opposition party stepped up to defend May against Trump's comments.
"He's looking forward to meeting Melania", May said of her husband, The Sunday Times reported "He has been out and bought a new suit".
The Sun said the interview was conducted Thursday in Brussels, before Trump travelled to Britain.
"For the majority of British people who support Brexit, this could scarcely have come at a more welcome or desperate time", Mr Delingpole said.
Despite the welcome from May, many Britons are opposed to Trump's visit.More news: What President Trump said about May, Brexit, and 'England'
During a press conference in Brussels after the North Atlantic Treaty Organisation summit, Mr. Trump appeared to criticize Ms.
He is then due to spend two days at golf courses he owns in Scotland before travelling to meet Russian President Vladimir Putin.
The blog Red State said it would be "interesting to see how the Brits react to this".
USA political website The Hill also focused on Mr Trump's comments about "millions and millions of people" coming to Europe from the Middle East and Africa.
The shadow policing minister, Labour MP Louise Haigh, said, "It has emerged that officers being accommodated in Essex are sleeping on cots in squash courts, 100 female officers with four toilets between them, likely to be sleeping on mats tonight, 300 male officers with five toilets between them".
The Hill noted that migration levels to Europe had declined since 2015, when more than a million people, many fleeing the Syrian civil war and other conflicts, arrived.
Mrs Trump was greeted by Mr May when she stepped out of her vehicle.More news: Thai Navy May Put Elon Musk's Mini-Submarine to Use. One Day