In transcripts from an interview with the Wall Street Journal, the US President said he wants the new relationship with Britain “as soon as it’s appropriate to have it kick in”.
Mr Trump confirmed he would be seeking a cross-sector deal. “It would include everything,” he told the WSJ.
Asked if that meant a deal on financial services, he said: “It would be very all-in.”
The President was also clear he wanted US agriculture to have more access to British markets, while criticising the EU’s trading relationship with the US on food products.
Critics have raised fears British markets could be opened up to US food products currently blocked by EU food standards rules, including controversial chlorine washed chicken.
The President said: “I have a very good relationship with the EU people and all, but they are very, very protectionist.
“Our farmers and others can’t even deal with (them) you can’t sell in. It’s very unfair. And that’s what I’ve been talking about for a long time.
“It’s so stacked against the United States.”
He added: “The EU was conceived to the point that they wanted to do something to compete with the United States.
“You could say that’s a friendly act or an unfriendly act. But it’s very protectionist. We have farm products that you just can’t get into the EU. And we don’t do that to them.”
The interview on 25 July came as International Trade Secretary Liam Fox was in Washington for talks with US trade representative Robert Lighthizer.