"I did give, Theresa, who I like - I did give her my views on what she should do and how she should negotiate, and she didn't follow those views", Mr. Trump told the Sun.
The interview was published as May greeted Trump at a lavish welcome reception at Blenheim Palace, the birthplace of Winston Churchill.
The plan put forward today would see the UK form an associate agreement with the EU, would effectively keep the UK in the customs union and single market for goods, and could allow EU migrants to work in the UK without a visa - albeit on a temporary basis.
But the plan has infuriated fervent Brexit supporters, who think it would limit Britain's ability to strike new trade deals around the world.
"He is thankful for the wonderful welcome from the Prime Minister here in the U.K".
"If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal", Trump told The Sun.
"As he said in his interview with the Sun she "is a very good person" and he 'never said anything bad about her, '" Sanders said in a statement to The Hill.
Fielding questions following the North Atlantic Treaty Organisation summit in Brussels, Mr Trump was asked his views on Britain's withdrawal from the European Union, suggesting it may deliver a softer Brexit that was not what the public wanted.
It also moots the idea of developing new arrangements for technologies such as artificial intelligence, noting that they are vulnerable to non-tariff barriers.
"They voted for us to take back control of our money, our law and our borders and that's exactly what we will do".
The plan was agreed by Prime Minister Theresa May's cabinet last week - only for two top ministers to quit in protest at its provisions to adopt European Union rules on trade in goods.
"I think he's got what it takes".
Trump's comments will plunge the transatlantic "special relationship" to new lows, making for extremely awkward talks with May.
The Government has been accused to lying to MPs faces about their plans for Brexit, according to Brexit Central.
Britain and the European Union would maintain a "common rulebook" for goods to ensure smooth trade including in agricultural, food and fisheries products. Such an approach would avoid disruption to automakers and other manufacturers that source parts from multiple countries.
Protesters gathered outside the entrance to Blenheim Palace ahead of the scheduled dinner. Johnson was slightly more diplomatic in his resignation letter, warning May that Britain was "headed for the status of a colony" within the EU.
Free trade would not apply to services, which account for 80 per cent of the British economy.
Britain wants a new treaty allowing it to continue using EU internal security measures such as the European Arrest Warrant and to participate in agencies such as Europol.
Trump said, however, that he "feels unwelcome" in London due to the thousands of people expected to protest in the British capital, as well as other cities. The European Court of Justice will no longer have jurisdiction in Britain, she says.