The 24-year-old winger suffered the injury after scoring in Liverpool's 3-1 Merseyside Derby win over Everton on Saturday
The 24-year-old Senegalese winger -- who has scored 13 goals this season and whose absence when on Africa Cup of Nations duty coincided with a slump in Liverpool's form -- is due to have his swollen knee examined further.
Mane suffered the injury after scoring in Liverpool's 3-1 Merseyside Derby win over Everton on Saturday and had to come off.
Liverpool have eight matches remaining in their Premier League campaign -- beginning with Wednesday's home game with Bournemouth.
Presently they are third but only a point ahead of Manchester City, who have a game in hand, and six points clear of fifth-placed Manchester United, who have two games in hand.
"Unfortunately that is possible but why should I say it now when I don't know?" said Klopp when asked at his eve of match press conference whether Mane could miss the rest of the season.
"The knee is swollen and we have to wait for the final assessment. It is not 100 percent clear.
"The only thing I can say for sure is that he will not be available for tomorrow (Wednesday).
"It is not very positive when it is like this. I cannot say at this exact time so we have to wait."
Aside from Mane, Klopp will also have to do without key players in English international duo Adam Lallana and Jordan Henderson, against a side who came from 3-1 down to beat them 4-3 in their previous meeting.
"As a manager I can't really remember the last time I had all the players available and the decisions to make were really difficult," said Klopp.
"My job is to find solutions. This is a good situation: we have 59 points, we are in a nice position -- yes a few teams have played less games than we have but they cannot win them all because they have to play each other.
"The whole season is to prepare the finish and this is the finishing part of the season. Eight games to go. We expect results from ourselves.
"It is not about thinking 'How can we play perfect football?'. We need to get results, and the first thing I will think about is how we can defend (against) Bournemouth not how can we create 27 chances?"