Trump's remarks, made in a bombshell interview with The Sun published on Thursday during his first visit to Britain as US president, are an explosive intervention into British politics that seems likely to cause political chaos and imperil the prime minister as she attempts to negotiate Britain's exit from the European Union.
May's proposal quickly sparked a slew of high-profile political resignations from her Cabinet, including Foreign Secretary Boris Johnson and Brexit Secretary David Davis, over concerns the plans would leave the UK too closely linked to the EU.
"If they do a deal like that, we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal," Trump said, according to The Sun.
He added: "If they do that, then their trade deal with the US will probably not be made."
Trump personally criticised May's handling of Brexit, saying that her so-called soft-Brexit approach went "the opposite way" to what he had recommended and that it was "very unfortunate."
Trump attended a black-tie dinner at Blenheim Palace with May on Thursday evening, where the TV network ITV reports May planned to pitch the president on a free-trade agreement between the UK and the US after Brexit. But Trump's interview with The Sun now leaves that prospect in doubt — and puts May in a vulnerable position.
Many Conservative members of Parliament who support Brexit are already in open revolt over her proposals, which Johnson said would turn the UK into an EU "colony" — and Trump's remarks are sure to inflame their concerns. May is already believed to be dangerously close to a vote of no confidence by her party.
The prime minister's plan "will definitely affect trade with the United States, unfortunately in a negative way", Trump said.
"We have enough difficulty with the European Union. We are cracking down right now on the European Union because they have not treated the United States fairly on trading.
"No, if they do that, I would say that that would probably end a major trade relationship with the United States."
In a statement released late on Thursday, White House press secretary Sarah Sanders said: "The President likes and respects Prime Minister May very much. As he said in his interview with the Sun she "is a very good person" and he "never said anything bad about her." He thought she was great on NATO today and is a really terrific person.
"He is thankful for the wonderful welcome from the Prime Minister here in the UK."
Receive a single email every morning with all our latest news: Sign up here.
Also from Business Insider South Africa: