The US president was speaking to reporters at the Oval Office just hours after England's 3-2 victory over Mexico at the Estadio Azteca, which sent Thomas Tuchel's side into the World Cup quarter-finals.
"What a game that was, England and Mexico. In the two countries I don't know the players, although I think Kane is a great player," Trump said. "See, I played golf with him and I like him a lot.
"He's a good golfer, but he's really great. There was no reason for me to watch [England against Mexico] but you couldn't take your eyes off the game."
It is not clear where or when the pair are supposed to have played together, though both are known golf enthusiasts - Trump owns more than a dozen courses worldwide, while Kane has previously spoken about his own love of the sport.
The comments followed an earlier post on Trump's TruthSocial platform, sent shortly after Kane converted a penalty against Mexico for his sixth goal of the tournament.
"Harry Kane of England is a GREAT player!!!" Trump wrote.
It is the latest in a string of public endorsements from Trump for the Bayern Munich forward, whose penalty in Mexico City took him to six goals for the tournament, making him one of the standout performers of the finals so far.
England needed a battling display to see off Mexico, having gone down to 10 men before holding on through 11 minutes of stoppage time to book their quarter-final spot. Kane's composure from the spot proved decisive on a chaotic night in Mexico City.
Trump has made a habit of weighing in on major sporting events since returning to office, regularly offering opinions on football and golf despite limited familiarity with either nation's domestic game.
His remarks are likely to raise a smile among England supporters, even if the exact circumstances of any round of golf with Kane remain a mystery for now.