Mane picked up the injury in Liverpool's 3-1 win over Everton on Saturday. A prolonged absence for the Senegal international could have far-reaching consequences for his team's chances of finishing in the top four.
The 24-year-old's departure to the African Nations Cup in January coincided with Liverpool's worst run of results all season - the club won just one of seven games in all competitions without him.
"It's not 100 percent clear. We have to wait a little bit. I can say for sure he won't be available for tomorrow," Klopp told a news conference on Tuesday. "The knee is swollen. We wait for the final assessment. It's possible (his season could be over) but why should I say that now?"
Liverpool will also be without skipper Jordan Henderson and midfielder Adam Lallana for the visit of Bournemouth, but forward Daniel Sturridge is back in training for the first time since the start of February.
Striker Divock Origi came off the bench to score Liverpool's third goal against Everton, and Klopp indicated that the Belgium international could start on Wednesday.
Read the full article on eurosport.co.uk: Mane faces missing rest of season