I don't think Osimhen will opt for Saudi league if he doesn't get go offer from EPL teams. Before his move to Galatasaray, he had opportunities to move to Saudi but rather he opt for the least European football league still open by then which was Galatasaray, after Chelsea tried to used the deadline as an advantage to get him sign a cheap contract which he turned down.
Now another June/July transfer window is closed by and he is among the headlines after is consistency even in the Nigeria team, where he hi like the best player always giving his all to the team. He would definitely get more attention this coming transfer than this previous one.
That's already clear from Osimhen's actions. The man turned down a €30 million-a-year offer from Al-Ahli last summer (!!) and instead went on loan to Galatasaray, which is not one of the super clubs. He wants to leave a memory, not just get the bag of money. That says everything about his personality. He's also the hottest scorer on the market going into the summer, thanks to his 26 goals in 30 games this season and his play for Nigeria. Arsenal is interested, Manchester United needs someone just like him, and Chelsea might even come back with a real offer after messing up the first time. His release clause has dropped to just €75–81 million, so you can bet that there will be a real fight this summer. I would even say he could be the most important signing for the EPL since Haaland. Arab? That is, unless every door in Europe shuts, which won't happen.
A number of clubs in the English Premier League are interested in signing Osimhen, so when the next transfer window opens, some of the Premier League's biggest teams may offer the Nigerian star big money. Earlier we have seen a lot of drama about Osimhen's change of team. Many active media confirmed that many clubs in Europe offered Napoli big money to sign Osimhen but Napoli rejected the money offer every time. As opposed to rejecting an offer of such a huge amount of money, we all thought that Osimhen's club might be making such a decision to ruin his career, but in the end we see him move to a club in the Turkish League. Now, as the transfer window approaches, there is more discussion about his team change, but this time at least I think we won't see much drama about his team change.