Donald Trump has said the UK will "probably not" get a trade deal with the US, if the prime minister's Brexit plan goes ahead.
He told The Sun the PM's plan would "probably kill the deal" as it would mean the US "would be dealing with the European Union" instead of with the UK.
Downing Street has not yet reacted to Mr Trump's remarks.
Theresa May has been making the case for a US free trade deal with Mr Trump, on his first UK visit as president.
She said Brexit was an "opportunity" to create growth in the UK and US.
Mr Trump also said that former foreign secretary Boris Johnson would make a "great prime minister", adding "I think he's got what it takes".
In his interview, he renewed his criticism of London Mayor Sadiq Khan over last year's terror attacks in the capital, saying he had done "a terrible job".
The president and his wife were given a red carpet reception at Blenheim Palace, Oxfordshire on Thursday evening.
They were at a black-tie dinner with Mrs May as news broke of his interview with the newspaper, which said it was conducted while he was in Brussels.
Mr Trump told The Sun newspaper that the UK's blueprint for its post-Brexit relations with the EU was "a much different deal than the people voted on".
He said the Brexit proposals Mrs May and her cabinet thrashed out at Chequers last week mean it would be "most likely ... we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal".
He also said he had told Mrs May how to do a Brexit deal, but: "She didn't agree, she didn't listen to me."
"I told her how to do it. That will be up to her to say. But I told her how to do it. She wanted to go a different route," he said.
The US president also said he was "cracking down" on the EU because "they have not treated the United States fairly on trading".
Mr Trump's comments came on the same day the UK government published its proposal for its long-term relationship with the EU.
The long-awaited plan is aimed at ensuring trade co-operation, with no hard border for Northern Ireland, and global trade deals for the UK.
At Thursday's dinner, Mrs May said that more than one million Americans work for UK-owned firms, telling Mr Trump: "As we prepare to leave the European Union, we have an unprecedented opportunity to do more.
"It's an opportunity to reach a free trade agreement that creates jobs and growth here in the UK and right across the United States."
On Friday, Mrs May and Mr Trump will go to watch a joint counter-terrorism exercise by British and US special forces at a military base.
The pair will then travel to Chequers - the PM's country residence in Buckinghamshire - for talks with the foreign secretary.
Extra security is in place to police the protests. More are planned for the second day of Mr Trump's visit.
The president and first lady will travel to Windsor on Friday afternoon to meet the Queen, before flying to Scotland to spend the weekend at Mr Trump's Turnberry golf resort. This part of the visit is being considered private.