While neither club has confirmed the move, it's been revealed the Georgia international has passed his medical.
Il Corriere dello Sport says he underwent 'secret' medical with Napoli and the Partenopei will announce his signing on July 1.
The 21-year-old has been playing for Dinamo Batumi since Russia's invasion of Ukraine.
Kvaratskhelia will be allowed to join Napoli as a free agent, with an announcement due when everything formalised on July 1.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!