“I may not agree with his philosophy, but I have a very good relationship with him.”
The President added the UK was being considered as the destination for the first international trip of his second term.
He told the BBC: “It could be Saudi Arabia, it could be UK. Traditionally it could be UK.”
Sir Keir most recently met with Mr Trump at Trump Tower in New York during the presidential campaign.
The pair also spoke on the phone following Mr Trump’s election victory, with Downing Street saying both men agreed the relationship between the UK and US was “incredibly strong” and would “continue to thrive”.
Following Mr Trump’s inauguration on January 20, Foreign Secretary David Lammy indicated Sir Keir would visit Washington within weeks.
