The Liverpool boss embraced the Tottenham striker after a 1-1 draw at Anfield on Saturday evening.
Indeed, Philippe Coutinho put the Reds 1-0 up at Anfield but Kane netted Tottenham's equaliser on Merseyside.
And Klopp couldn't help but give the 22-year-old a hug after the game.
The German usually reserves such embraces for his own players but this was a sign of the good sporting contest Liverpool shared with Spurs on Saturday evening.
A draw was, in the end, a fair result and Klopp and Mauricio Pochettino have shared two good games this season that both ended in stalemates.
Kane's goal extended his lead at the top of the Premier League scorers' charts and the Tottenham man's brilliance in front of goal this campaign is becoming unmatched.
Jamie Vardy is yet to play this weekend, of course, and could well net more than once for Leicester on Sunday.
But it's no wonder Klopp showed his appreciation of Kane at Anfield - the Liverpool manager probably wouldn't mind having him alongside Daniel Sturridge!