Not sure if Mane will return to Liverpool in a transfer or buy-back, but if only on loan it seems a possibility. After all, Mane also at Bayern Munich doesn't have a good bond with other players maybe only with Sane, because with disputes between players, of course their gameplay is not optimal. But from different information, I read that Mane will probably play in the Saudi Professional League whether that's true or not, but I personally feel that Mane will still stay at Bayern Munich.
Mane’s performance in Bayern Munich is not something impressive to when he was in Liverpool. Maybe because he don’t get enough playing time or hasn’t bond well in the team. The few matches he got to play for the team has been commendable not until when he had clash with Sane and it affected him both in the team and also in the field of play. Going back to Liverpool will not be a bad idea for him but if he’s linked to Saudi league, he might probably prefer to join Saudi side than returning back to Liverpool. His fate at Bayern is undecided for now since we haven’t heard any news about his transfer yet or maybe staying back.