The US president hailed the “very special relationship” he had developed with Theresa May as the pair met for talks on the margins of the G20.
Mr Trump said he expected an agreement on new trading arrangements with Britain that was “very powerful” and would be great for both countries.
Mr Trump said: “There is no country that could possibly be closer than our countries.
“We have been working on a trade deal which will be a very, very big deal, a very powerful deal, great for both countries and I think we will have that done very, very quickly.”
He added: “Prime Minister May and I have developed a very special relationship and I think trade will be a very big factor between our two countries.”
Mr Trump said he “will be going to London”. Asked when, he replied: “We’ll work that out.”