Mr Trump, who is visiting the UK for a three-day state visit on Monday, said he thinks the former foreign secretary would be "excellent" as a successor to Theresa May.
Speaking to the Sun, Mr Trump said: "I think Boris would do a very good job. I think he would be excellent."
The President added: "I like him. I have always liked him. I don't know that he is going to be chosen, but I think he is a very good guy, a very talented person.
"He has been very positive about me and our country."
Mr Trump also said other candidates have approached him in a bid to secure his endorsement.
He said: "Other people have asked me for an endorsement too. I have been asked for endorsements".
He added: "I could help anybody if I endorse them. I mean, we've had endorsement where they have gone up for 40, 50 points at a shot.
"Now that is here, but I understand over there would be a great endorsement."
Mr Trump has previously spoken of his admiration for Mr Johnson and Brexit Party leader Mr Farage.
According to the Times, senior White House officials are preparing for a meeting between Mr Trump and Mr Johnson.
Mr Farage, however, said he has been "banned" from meeting Mr Trump during his visit.
Speaking to the Daily Express, Mr Farage said Mr Trump's entourage had been told by No 10 not to meet him.
Mr Farage told the Express: "Isn't that absolutely bizarre? Doesn't it sum up why British politics needs to change?"