I believe Napoli cleared this rumor, and the club has stated several times that they were unwilling to trade him. So, Kvarat has no reason to leave the club because he is still under a long-term contract with Napoli. But he can approach his squad about the prospect of releasing him, and again, I doubt Napoli will release him for a reasonable amount.
Kvarat was more than just a fine winger, and PSG is open to new alternatives. Partenopei is the party that will shape his future. I'm concerned about PSG's reaction to the crazy rumors that have arisen in public about the club and Kvarat.
Well Antonio Conte has confirmed that Khvicha Kvaratskhelia has no intention of being sold, he is an important player for Napoli. However, his good performance with Georgia at Euro 2024 and being able to win the match even though he had to face Ronaldo has made a number of clubs such as Liverpool and PSG increasingly interested in him. But it seems that Napoli really don't want to let go of their player and are trying to persuade him to stay at Napoli because he has The contract with Napoli is until 2027, but it seems like Liverpool and PSG are not giving up in continuing to persuade him until he finally decides what he wants.
Compared to staying as a Napoli and PSG player, if I were him I would choose to leave and join Liverpool, this will be a new challenge for him to play in the Premier League, where of course the competition is very tight, he has to get out of his comfort zone to gain new experience as a football player he must have a lot of experience in order to become a successful player.