If we talk about Osimhen's personal desires, he really wants to leave Napoli. The reason is that after this season finished, from the news I read, Osimhen felt that he was no longer suitable to be at Napoli. The reason is, Osimhen had problems with Napoli due to video content uploaded by Napoli which seemed to mock Osimhen.
Didn't that incident happen a long time ago? Yeah it wasn't a nice action taken by Napoli side. I would also be disappointed if I was Osimhen. However I thought they found a middle way later on.
As far as I know, Kvaratskhelia is much more keen on leaving compared to Osimhen. Because of the things going on among him, his agent and the team recently I mean. But of course, Osimhen would also be okay to sign for a solid team at the earliest opportunity.
He didn't want to sign a long-term contract with Napoli. Therefore he might leave this summer in case of a sensible offer. Maybe an offer by PSG? I would say Chelsea too but they don't look interested recently.