In my opinion, Osimhen will relatively stay with Napoli because so far no team is really serious about signing him other than just saying they are interested. Napoli will have to keep their star players with them for next season if they want to strengthen themselves as the strongest team in Serie A next season.
PSG is indeed eyeing the Napoli striker as an alternative player to replace Mbappe. However, they are aware that this player actually has no desire to move, as well as Napoli who do not want to let go of the player who brought him in and contributed greatly to winning the Italian Serie A last season. Because of that, Napoli provides quite a fantastic price tag for clubs that want Oshimen. So this might make other clubs not focus anymore on these forward players.
Oshimen is already very comfortable in Napoli, so it's impossible for him to leave easily. His career at Napoli has been very good, with a salary offer of €5,450,000 annually, which is quite a large value with the facilities that Oshimen got while still contributing to Napoli. Even though Oshimen is still very young and has experience that can be gained, I'm sure he will not miss the comfort that Napoli has given him.