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".
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".
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