The president later played down his remarks during the joint news conference with May, saying he understood why she had found the advice "a little bit tough".
Speaking to the BBC on the Andrew Marr Show on Sunday morning, the Prime Minister finally revealed what the President had said: "He told me I should sue the EU".
"Oh I think we're going to have a great trade deal, I've really no doubt about it", Trump said in the interview.
Trump said Queen Elizabeth, 92, was a "fantastic woman", adding: "up close, you see she's so lovely. and she's got a lotta years left".
"We need to ensure there is a balance between protection and public safety and the public's right to peacefully protest".
The President had previously revealed that he would have dealt with Brussels "much differently" than the Tory leader, telling The Sun newspaper: "I actually told Theresa May how to do it but she didn't agree, she didn't listen to me..."
Her decision to reveal Mr Trump's freakish suggestion will be taken as a small act of revenge after his incendiary interview stoked the Brexiteer rebellion against her proposals to soften Brexit by keeping the United Kingdom in parts of the single market.
A giant inflatable "Trump baby" will not be allowed to fly over the USA president's Turnberry golf course when he visits over the weekend, Police Scotland have said. It's not just a few hardline eurosceptics, it's the nation at large that feels it voted to leave the European Union and it expects to leave the European Union, it doesn't want another prime ministerial fudge.
The two leaders have disagreed on how May should handle the exit from the bloc, with Trump frequently haranguing her to hurry the process.
Labour MP Ian Murray, a member of the People's Vote campaign, said the British people needed a vote on the final deal.
May weathered the resignations of her Brexit and foreign ministers last week over her proposals for Brexit.
When asked on Sunday if she would stand if a Conservative Party leadership contest was triggered, May declined to directly answer saying: "I am in this for the long term".
Pro-Brexit lawmakers are expected to use a debate on Monday on customs legislation to try to force her to harden up her Brexit plan, while a debate on trade on Tuesday will see pro-EU lawmakers push for even closer ties with the bloc. Along with Mr Johnson, the man who had been leading the Brexit negotiations, David Davis, also quit in protest.
"We could have said "Let's stay where we are and see what happens" and risk actually ending up with a chaotic leaving which I don't think is in people's interests".
The UK is due to leave the European Union on March 29, 2019.
Then you're stuck, '"she added".