But Trump poured cold water on May's offer.
At a press conference on the first day of the USA president's visit to the UK, Mr Trump attempted to fix the damage created by his embarrassing newspaper interview by heaping praise on the prime minister and telling her "whatever you do [on Brexit] is OK with me".
"There is no stronger alliance than that of our special relationship with the United States and there will be no alliance more important in the years ahead. I have a lot of respect for the prime minister", Trump said.
"If they do that, then their trade deal with the United States will probably not be made".
In many ways, they're more like the Democrats in the United States.
Trump, who has compared the June 2016 referendum in which a majority of British voters supported leaving the European Union to his own election that year, accused May of abandoning British voters with her Brexit plans. The newspaper released lengthy clips of the interview that showed Trump saying that May did not take his advice on how to handle Brexit, saying she "wrecked it".
May has insisted that her Brexit plan will allow Britain to strike its own lucrative trade deals with countries like the USA after leaving the European Union in March next year. But at the Chequers news conference, Trump said he had been responding to the Sun's question about Johnson as a possible prime minister, adding: "He has been very nice to me".
He said that May's new, softer approach to Brexit - which would leave Britain sticking to a "common rulebook" with Brussels on goods - would kill off the chances of a much sought-after USA -U.K. trade deal.
Nevada to execute inmate with fentanyl in U.S
Nevada has struggled to find drugs to carry out Dozier's execution because of resistance from manufacturers. Dozier, who attempted suicide in the past, has said he prefers execution to life behind bars.
Their meeting lasted almost an hour and was the final engagement in Mr Trump's two-day working visit to the UK.
"I partially won an election because of immigration", he said, also pointing to Italy's recent vote, in which Giuseppe Conte took government after campaigning on a populist anti-immigration platform. "She said: "Don't worry, it's only the press".
"Almost winking at the big man for a trade deal", someone else wrote. However, under the blue skies of the Chequers' garden, he said their relationship was "the highest level of special". Over 50,000 people are expected to descend on central London on Friday to protest the leader's visit.
The president also hit out at immigration into Europe, linking it with crime. Interviewed before he left Brussels for the UK, Trump had accused May of ruining what her country stands to gain from its Brexit vote. Trump said Khan has done a "very bad job on crime" and a "very bad job on terrorism".
President Donald Trump wants to redesign Air Force One. He was heralded by military bands on his arrival at the 92-year-old monarch's home where her grandson Prince Harry married US actress Meghan Markle in May.
By Friday afternoon, Mr. Trump appeared to backtrack, saying he'd had an opportunity to learn more about Ms.
Her trip to Europe marked the former model's return to the worldwide stage after she was hospitalized for a kidney condition in May and dropped out of public sight for almost a month.
"I love the United States but I love getting along with Russian Federation and China and other countries".