"I would love to say that I think this is going to be a hugely successful visit but I think it's going to be very hard", he said at a pro-Trump gathering in parliament.
The Jameson in Hammersmith has rebranded itself The Trump Arms for the US President's visit.
"I just want the people to be happy".
Asked about Trump's comments at a hastily-arranged meeting with journalists, May said she was delivering wishes of the British people.
"I'd like to see them be able to work it out so it could go quickly".
"There is no stronger alliance than that of our special relationship with the USA and there will be no alliance more important in the years ahead", the British leader said.
Mr. Trump, however, suggested before leaving a North Atlantic Treaty Organisation summit in Brussels on Thursday to head for London, that Britons in general agree with his policies, in particular his tough stance on immigration.
Trump is not expected to spend time in central London.
May will host Trump and tuxedo-clad government ministers and representatives of fund managers BlackRock and Blackstone Group, as well as Arup and drinks manufacturer Diageo, for a dinner of Scottish salmon, beef and strawberries and clotted cream ice cream to discuss post-Brexit trade.
She's planning to attend anti-Trump protests. After the visit, Trump will decamp to Finland for a one-on-one with Russian President Vladimir Putin on July 16.
Churchill spent three weeks at the White House, cementing his close ties with Roosevelt and forming the basis for future relations between the US and Great Britain.
Tens of thousands of people are expected to march through London in protest against Mr Trump's visit and some of his actions during his first 18 months in power.
Later in the day, the President will head to Windsor Castle, where he will have a tea with the Queen.
His "America First" policies, including the decision to pull the United States out of the Paris climate accord and the nuclear deal with Iran, have brought him into conflict with Britain's leaders over issues of real substance.
There are also plans for protestors to gather close to the United States ambassador's residence in Regent's Park, where Trump and his wife, Melania, will stay overnight on Thursday.
10 Downing Street said she would be meeting with schoolchildren and veterans on Friday, accompanied by Philip May, U.K. Prime Minister Theresa May's husband.
He is also expected to visit Scotland - where he owns two golf courses - before heading back to the US.