Napoli's manager Antonio Conte are welcome for every team interested for signing Osimhen but recently still not any teams have give official bid offer interested with Napoli's central forward. Its make bit difficult position for Antonio Conte because he need much money for signing his interested striker Romelu Lukaku and Chelsea have announce for selling him without any swap option.
What's actually in Conte's head, Osimhen is better than Lukaku. It's really selfish that Conte want to sell a good player just because he want to sign his favorite player, he's nothing different with Ten Hag that sell Ronaldo and sign Netherlands players.
Only a few of the tens Barcelona, Real Madrid, and PSG rumors were real; the rest were cheap fake rumors. This means the media spread and exaggerated fake rumors for their own gain. If Napoli didn't want to sell Kvarat, their anger was clear.
Conte says Kvarat may be involved in his next Napoli project. Napoli repeatedly denied selling their players, but the media kept spreading the story.
As you said, the media aggressively predicted Napoli would sell Osimehn, but it never happened.
Barcelona lack of funds.
Real Madrid already have many strikers.
Only PSG is possible, if Kvara really want to leave Napoli.
However, since Conte says like that, I think Kvara will stay in Napoli.