Galatasaray are interested in keeping Osimhen because Osimhen is a great player but Osimhen wants to play for a big club in Europe and perform his best there. Last season he had a big chance to move to a top club in the English Premier League and big clubs were ready to pay big money for him but at that time his club did not help him so he had to move to another league outside Europe. When the transfer market opened this season there were rumors that either Manchester United or Liverpool would buy this player but as time goes on it seems that maybe his dream of moving to a big club in the English Premier League will not come true this season and he may have to stay at his current club for another season. The longer he stays at a club outside Europe his market value will gradually decrease.
Osimhen has proven himself to be a much-needed player at Galatasaray. He even finished as the top scorer in the Turkish league last season. So it's no surprise that Galatasaray has now agreed to pay Osimhen's release clause to acquire him. However, Galatasaray can't pay the full price all at once due to regulatory issues or something. However, an agreement has reportedly been reached regarding installment payments, which will be finalized at the end of the season. So I think Osimhen will definitely be joining Galatasaray soon.
Osimhen's dream is to play in a bigger league like the Premier League, and in the past few seasons, he received offers from English clubs and Ligue 1 side PSG. However, Napoli rejected these offers, leaving Osimhen to stay and then be loaned to Galatasaray. Fortunately, he's comfortable there, and now he's keen to join the club.
He feels comfortable at Galatasaray because he didn't find comfort playing for Napoli, so last season, his loan to Galatasaray wasn't a problem. Osimhen is still quite young, only 26 years old, and it's clear that to advance his career, he needs a club playing in a more competitive league like the Premier League. Several Premier League clubs, such as Chelsea, Arsenal, and Manchester United, are quite interested in signing him, but they haven't reached a mutual agreement yet.
A deal between Napoli and Galatasaray is currently close to being reached, but since nothing has been signed yet, anything is possible. In fact, according to several sports reports, Napoli has opened talks with Al Hilal, an Arab League club, who is also interested in signing Osimhen. Of course, Al Hilal has a better financial position than Galatasaray, so if Galatasaray can't meet Napoli's demands, the deal could fall through.
I don't see that deal coming to pass, because Osimhen have rejected the deal and wants to continue playing in Europe. Napoli is not after the interest of Osimhen due to their own selfish reasons and the hatred on the player, but they cannot decide his future for him, because he has the right to go to any club of his choice and not Napoli to choose a club for him.