While Osimhen was really close to leaving Galatasaray and Napoli and joining the Saudi League and there is even news about him leaving Galatasaray for the other teams in Serie A, it seems this player is even about to extend his contract with Galatasaray and staying there after ending his loan time. While Galatasaray got Osimhen for a loan but they are happy to have this player in the team and that's why they want to have Osimhen permanently.
Osimhen was close to joining PSG and Chelsea too but he is currently playing for Galatasaray on loan.
However, Galatasaray should pay 120 million euros for him which is a huge amount of money.

I think Napoli can not get 120 million for Osimhen and the real price that Galatasaray is ready to pay is 50 million considering not the easiest character of Osimhen, but because of Osimhen's good game, his transfer value is growing and by the summer may reach 75 million, so Galatasaray will not be easy to keep him.
I think Galatasaray have not had such expensive transfers before and even if Osimhen wants to stay in the Turkish league, Napoli probably won't want to loan him out for a second season and will try to sell him to a place where they will pay more for him, and that is the Saudi league.
At Galatasaray, the Nigerian striker has been in excellent form, including a brace in a 3–2 win over Tottenham in the Europa League. Although Galatasaray wants to keep Osimhen for the long term, the ability to convince him to stay is still a big question mark. Will he accept to stay in this small arena, is he satisfied with the small salary here? And 120 million euros is a huge amount for the Galatasaray club.
In my opinion, the Premier League will be the next ideal place for Osimhen to develop his career. The uncertainty over Osimhen's future could work to the advantage of Premier League sides still interested in the star. Manchester United, Chelsea, and Arsenal will be in the running to monitor Osimhen, with all three clubs likely to look to bolster their attack in the summer transfer window.