I don't think it is possible for Sadio Mane to play for Liverpool again, the club has already moved on after his exit, so they would be better off signing new players and try to build a team around them, rather than bringing back players who gave their best to the team and have already left for a different challenge. Sadio Mane didn't have the best first season in Bayern Munich, but i don't think he is ready to leave just yet, i know that the altercation with Leroy Sane makes it somewhat tricky as the club might want to sell one of them, which would prolly be Mane, but since the transfer window opened, there've been no news on Mane leaving the German champions.
Exactly because of his performance last season Liverpool wouldn't sign him again in their craziest dreams. That is not going to happen and even though I like Mane as a player a lot and he was the perfect complementary player in the offense for Liverpool, he doesn't really have versatile qualities that make him valuable in games that require some flexibility.
Even though Sadio Mané exit from Bayern Munich is set but most chances now he will be not coming back into Liverpool with few other clubs in Premier League are set to talk about his availability which is good because he was doing good here in Premier League and his sudden exit have bad impact on his performance with Bayern Munich is completely different place for player like Sadio Mané and his all season were not as expectations which is another big problem and most chances things will be not good for them to be in Liverpool.
There is no doubt about his quality but with this Liverpool is now doing things with completely different way which is surely not suitable for him but as we have rumors most chances he will be in action in next season here in England with any other good club which will be also good for his fans.