The Senegalese forward, 24, was forced off after challenging Leighton Baines for the ball during the second-half of Liverpool’s 3-1 win over Everton at Anfield.
Klopp conceded after the match that it was “pretty much impossible for him to play again this season” and the player is not set to travel to London on Tuesday for an operation to repair the meniscus in his left knee.
Mane has been one of Liverpool’s best players this season and he is expected to be side-lined up eight weeks, which at least means he will return for the start of Liverpool’s pre-season campaign, which begins in July.
It has been reported in the Liverpool Echo that Mane has suffered similar injuries to his knee this season, without requiring surgery.
However, a scan after the Everton match confirmed that a minor operation was now required, ruling the player out for Liverpool’s remaining six Premier League matches.
Mane, a £34m summer signing from Southampton, has started all but six of Liverpool’s matches this campaign.
In his absence the club have won only once – this weekend against Stoke City – drawing three times and losing twice.
The forward has scored 13 goals in 27 league appearances for Liverpool this term, his highest goal return since the 2013/14 season when he was playing in the Austrian Bundesliga for Red Bull Salzburg.