Trump told the newspaper he had advised May on how to conduct Brexit negotiations, "but she didn't listen to me".
The EU maintains that existing British red lines - no jurisdiction of the European court of justice, no free movement of people - mean the only option is a free-trade agreement, similar to those Brussels negotiated with Canada or Korea - a point of conflict with the United Kingdom that is subtly restated in Barnier's tweet. But EU diplomats who heard early outlines of the plan said it sounded too close to earlier proposals that were rejected previous year.
The comments from Mr Trump will send shockwaves through Westminster - and emerged as the prime minister hosted him at a lavish banquet at Blenheim Palace, the birthplace of Sir Winston Churchill.
But as the government finally announces its negotiating stance, which is widely seen as a less radical departure than businesses and pro-EU campaigners had feared, the focus will be on Brexit supporters.
The White Paper is based on the painfully brokered compromise struck by Theresa May's government last Friday, over which Foreign Minister Boris Johnson and Brexit Minister David Davis resigned earlier this week.
Trump came down firmly on the side of the Brexiteers.
Mr Trump went further and suggested to the Sun Mr Johnson was "a great representative for your country". I helped take the EU Withdrawal Bill through the House of Commons and we have got that bill through the House of Commons and the House of Lords, so through all of Parliament.
Donald Trump has warned Theresa May her Brexit blueprint will "kill" hopes of any future trade deal with the US. "If they do that, then their trade deal with the USA will probably not be made".
In response, Mrs May said the proposal was "delivering on the vote of the British people to take back control of our money, our laws and our borders".
Other eurosceptics who want a clean break with the bloc are also livid, prompting speculation they may launch a confidence vote against May.
May insisted earlier Thursday that her plan was exactly what Britons had voted for in the 2016 referendum.
If accepted by the European Union, the proposal would "end free movement, taking back control of the UK's borders". "That is exactly what we will do".
Trump had already cast doubt on May's Brexit plans earlier in the day after a North Atlantic Treaty Organisation summit in Brussels, where he provoked a crisis session to force allies to raise their defense spending. "With a lot of resignations", Trump told a news conference at the North Atlantic Treaty Organisation summit in Brussels.
Trump's interview easily could overshadow the government's attempt to lay out plans for what it calls a "principled and pragmatic" Brexit.
"First of all, protecting the Common Travel Area so people can continue to travel freely between Britain and Ireland". Such an approach would avoid disruption to automakers and other manufacturers that source parts from multiple countries. That, UK officials say, will also include a protocol on the backstop for Northern Ireland.
Free trade would not apply to services, which account for 80 per cent of the British economy.
But while industry bodies decried the government's decision, many banks and insurers had already scaled back their expectations of continued full access to the European Union market after Brexitand started opening new hubs in continental Europe.
He acknowledged that some of the British proposals would cause difficulties, adding that there are things that the European Union can not do. She praised the friendship between the two allies, glossing over Trump's previous remarks that Britain was a "hot spot" in turmoil over Brexit.