Bayern Munich don't need to sign any player to fill Mane's place in the team. Yes, there is still a long time ahead until Mane's recovery from his injury. He is expected to return by mid February for now. They of course have many Bundesliga matches in the meantime - 5 matches. But I believe that Bayern Munich can still do just fine in the league in his absence. Because the usual team spirit is back and they have started to play much more effective as a team. Nagelsmann would find a solution to Mane's absence as a result.

It is just going to be very important for Mane to be able to play against PSG in the first leg. This will be a way more different match compared to the Bundesliga ones obviously. They need one of their critical players like Mane in the match to raise their chance to win.