The Georgian winger can start earning close to 6 million euros per season.
Napoli is working on extending the contract with Khvicha Kvaratskheliya.
According to Gianluca Di Marzio, the Neapolitan club has contacted the winger's agents to discuss the possibility of signing a new player.
The parties will conduct a new meeting in a few years.
Napoli has made a proposal for a new contract while still in the limelight. If accepted, the Georgian footballer will be able to earn 6 million euros on the river with bonuses settled - like Romelu Lukaku.
The final clash between the sides will take place after the national break in the national team matches.
In the current season, Khvich has 8 matches for Napoli in all tournaments: 3 goals and 2 assists in this round.