It looks like Napoli are quite likely to keep Osimhen this summer. At least for now. Because there is no rumour regarding him to sign for another team these days. However there might be a chance for PSG to think of bringing him depending on Mbappe's situation. When they lose a player like Mbappe they need to bring another top player to try to make up for that.
Vlahovic has been rumoured with PSG maybe but in this case I think PSG can change their route to Osimhen instead. PSG are going to get 300 million euros as a transfer fee from Al-Hilal if Mbappe signs for them. They can surely use this money to sign a player like Osimhen.
Paris Saint-Germain is associated with any more or less large transfer and in most cases still the transfer does not happen. It depends more on the position of Osimhen himself, whether he is ready to change the Italian championship to French right now. So far, probably not, especially since both Napoli and Paris Saint Germain participate in the Champions League and I think that Osimhen's ambitions as a player are still higher than participation in Ligue 1 and Paris Saint Germain, and Paris Saint Germain is unlikely to buy a player with the expectation of only one season, but most likely with a good season without injuries, Osimhen is unlikely to stay in Napoli for more than 1 season.