The German is currently planning for his first pre-season with the Reds after taking over from Brendan Rodgers in October.
Klopp has started getting his players through the door pretty early on. Marko Grujic was signed last January, Joel Matip after that while Loris Karius completed his move from Mainz last month as the Liverpool manager is putting something of his own stamp on this team.
The Mirror reported at the end of last month that the Napoli striker would like a switch to Merseyside after a stunning season in Serie A, where he scored 36 goals in 35 games.
But Higuain may not be the only person in Klopp's mind as he watched Angel Di Maria inspire Argentina to a 2-1 win over Chile in a rematch of the final from last year.
Liverpool are said to be in the market for a left-back, so he could have been watching Eugenio Mena - Chile's left-back from Sao Paulo FC - one doubts Klopp is even thinking about Argentina's Marcos Rojo - currently of Manchester United.
For some Liverpool fans who are a fan of romantic reunions, there will be those hoping that Liverpool would want to try to lure Javier Mascherano back from Barcelona given there has been an element of uncertainty about his future. Some will feel the Reds need that bit more steel in midfield that has been absent since the Argentine's departure.
It will be interesting to see if any of the players on show last night are on Klopp's radar, or whether he was just simply enjoying a football game as he takes some time off ahead of what is a big season for both him and the club he manages.