Mr Trump said he had held a “great discussion” with Britain’s Prime Minister Boris Johnson on Monday.
It is not the first time Mr Trump has spoken of the potential for a trade agreement after Britain leaves the European Union, but came as a senior US politician warned that politicians could block a future deal if the .
Mr Trump tweeted: “Great discussion with Prime Minister @BorisJohnson today. We talked about Brexit and how we can move rapidly on a US-UK free trade deal.
“I look forward to meeting with Boris this weekend, at the @G7, in France!”
The new resident of Number 10 spoke with his American counterpart in July, when Mr Trump said they were working on a “very substantial” post-Brexit trade agreement.
The president said: “You know we can do with the UK, we can do three to four times, we were actually impeded by their relationship with the European Union. We were very much impeded on trade.
“And I think we can do three to four or five times what we’re doing.”
Speaking last month, the president referred to Mr Johnson as “Britain’s Trump”, saying he was “tough and smart”.
He said: “I think we can have a great relationship and Boris is going to be a great prime minister,” he said. “I predict he will be a great prime minister.”
Meanwhile, Senate Democratic leader Chuck Schumer has written to US Secretary of State Mike Pompeo warning that Congress could work on a cross-party basis to block a deal if a hard border is introduced on the island of Ireland.
Mr Schumer, in the letter also sent to Foreign Secretary Dominic Raab, said: “I write to express my inveterate opposition to any prospective trade deal with UK that either undermines the landmark Good Friday Agreement or facilitates a return to a hard border.
“As we approach the fiftieth anniversary of the traumatic events that precipitated the long and difficult period known as ‘The Troubles’, all stakeholders would do well to reflect on the hate, violence, injustice, lawlessness and societal upheaval of that time — and of the extraordinary transformation ushered in by the Good Friday Agreement.
“America had a proud role in facilitating and brokering the Good Friday Agreement, and America remains a vital guarantor of it.
“This is no small responsibility and it must not be shirked.”