Trump accused the British political leader of "killing" chances of a USA trade deal by ignoring his advice on Brexit and taking her own, "softer" approach.
Trump also expressed disappointment with May's handling of Britain's withdrawal from the EU.
"I'd like to see them be able to work it out so it could go quickly", he said.
"The people voted to break it up so I would imagine that's what they'll do but maybe they are taking a bit of a different route so I don't know if that's what they voted for".
Trump will largely avoid travelling around the capital and other major cities due to the anticipated protests and his meetings will take place at various country estates or palaces. A YouGov poll on Wednesday showed 77 percent of Britons had an unfavourable opinion of the president and just 50 percent thought his visit should go ahead.
"You have a mayor who has done a bad job in London".
Meanwhile Amnesty International unveiled a 15-meter banner on Vauxhall bridge opposite the US Embassy branding him a "Human Rights Nightmare".
Trump insisted, however, that most in the United Kingdom were "delighted" about his visit even as he took a shot at London mayor Sadiq Khan for not taking a harder line on immigration and painted the city as a hub for terrorism.
"The spirit of friendship and cooperation between our countries, our leaders and our people, that most special of relationships, has a long and proud history".
He said: "The government has been pretending that its document doesn't make trade deals any harder, and Donald Trump has just cut through that, and says it does".
Trump told The Sun he felt her approach of keeping some ties to the European Union would "affect trade with the United States, unfortunately in a negative way", and referenced his administration's combative trade posture with the EU.
May weathered the resignations of her Brexit and foreign ministers earlier this week over the proposals.
Mr Trump had already cast doubt on Ms 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 defence spending. Trump has denied any collusion with Russian Federation.
The six-metre balloon has also received permission to fly over Scotland, when Trump travels there for a private stay over the weekend.
- The pair will then travel to Chequers, the Prime Minister's country residence, for what is being billed as "substantive bilateral talks on a range of foreign policy issues" during a working lunch. His late mother hailed from Scotland, and he owns two luxury golf courses there.