He told The Sun newspaper that May'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.
"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 US," she said.
Trump told The Sun that conducted the interview while he was in Brussels for the North Atlantic Treaty Organisation (NATO) summit, that UK's blueprint for its post-Brexit relations with the EU was "a much different deal than the people voted on".
He said he had told May how to do a Brexit deal, but: "She didn't agree, she didn't listen to me... She wanted to go a different route." Trump also said he was "cracking down" on the EU as "they have not treated the US fairly on trading".
The news of his interview with the newspaper broke while he was at a black-tie dinner with May at Blenheim Palace, Oxfordshire on Thursday evening.
The US President along with First Lady Melania Trump were given a red carpet reception after they were earlier greeted by 1,000 protesters outside the US ambassador's residence in Regent's Park.
On Friday, May and Trump will watch a joint counter-terrorism exercise by British and US special forces at a military base. Later they will hold talks with the foreign secretary at Chequers -- the PM's country residence in Buckinghamshire.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)