The latest news I read, Napoli will reject the offer from PSG.
Kvaratskhelia is still an important part of Napoli team, Napoli mustn't agree to let him moving to PSG.
Moreover, Napoli will hire Conte, Conte must expect to have a big squad. It will be a big lose if Kvaratskhelia moves to PSG.
Napoli will ignore PSG offer
These would be the pieces requested by Antonio Conte for signing the contract with the Neapolitans.
https://www.transfermarkt.com/khvicha-kvaratskhelia/profil/spieler/502670
You omitted to specify whether Kvarat was interested in leaving Napoli. Kvarat can announce his wish to leave Napoli if he wanted but i think that the better for him to join in the PSG, and I believe this will force napoli to allow him to leave the club. This is Kvarat's chance to join PSG because he will play frequently in the UCL and improve his performance as a player. Playing in UCL is a very important thing these days.
There is no assurance that Napoli will return to its peak level soon. Kvarat is not pleased with Napoli's decision to sign Conte as a new appointment.
It is preferable for him to depart Naples. I'm sure Conte won't be too excited to use him as a winger. I'm not sure about Osimhen's future with the squad. Conte may also bring Lukaku to Napoli.
If used wide in a 3-5-2 formation, then he would be further away from the goal and even more frustrated.
Paris Saint-Germain are seeking a player to fire up the crowd after losing Kylian Mbappé and Kvaratskhelia would fit the bill.
I hope kvarat won't be stupid enough in missing this opportunity. Kvarat needs to improve his career. he shall not be stuck on the napoli. The competition in serie is just getting even stricter than before. Im still doubting that napoli's capability to get into the top positions again next season.