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.
That is like infinitely overestimating the attractiveness of the Saudi Professional League. Isn't it the truth that nobody really wants to go there unless they get paid these high damages how I would call it. It is not the league you want to play in when you have all these offers from other European top destinations. Ronaldo did it because it was so much money that he couldn't decline it. Neymar got 100 million for a few games only because he was injured all the time, but I bet that most of these players are on trips to European countries almost all the time.
Osimhen would have made a huge mistake going there and that was the reason why he said no. When you are in Europe as a player, you don't get forgotten too quickly. If he went to Al-Ahli, his reputation might have suffered a lot from that decision. In Ronaldo's situation it was different. His career was more or less over and he was able to get this huge amount of money. There wasn't much to lose for him.