So much so, that he helped persuade the club to spend what could turn out to be a club-record £85million on the Uruguay international, who Liverpool believe is the 'new Edinson Cavani'.
That's according to transfer guru Fabrizio Romano, who gave an in-depth look at the deal, which resulted in the 23-year-old striker joining the Merseysiders earlier this summer.
And, despite Klopp's amazement at seeing Nunez play for the first time, the Liverpool scouting department were long-term admirers of the South American.
"It's true that Darwin had a fantastic impact on Liverpool in the Champions League games between Benfica and the Reds," Romano said on his YouTube channel.
"Jurgen Klopp is a big fan of checking players in real, face-to-face games against Liverpool - and he was surprised by the fantastic striker.
"But in the Liverpool scouting department, they have been big fans of Nunez for a long time.
"They think of him as the 'new Cavani', a modern striker, a traditional No.9 in the position, but they know he has a lot of potential.
"They compare him to Edinson Cavani because, of course, his Uruguayan nationality, but also his approach on the pitch and his mentality."
Romano added that Real Madrid were 'really interested' in the centre-forward after missing out on Kylian Mbappe, but a deal became impossible due to the rules in Spain regarding non-EU players.
And Klopp's 'direct call' to the player was enough to convince him to join the Reds.