When he led Napoli to the Scudetto, Kvaratskhelia was one of the top wingers in Europe.
Gazzetta dello Sport journalist Bacho Tsalugelashvili suggests that Kvara is ready to leave.
He wants a new challenge and may see the Premier League as a great destination.
"Is Kvaratskhelia's agent talking to De Laurentiis? I believe the agent will meet the president next week," Tsalugelashvili told 1 Station Radio's 1 Football Night.
"However, either the contract renewal will materialize or Kvara will go to a top club. I don't know if it is Barcelona or another team.
"Could it be a Premier League club? I don't know. Liverpool are also interested in Kvaratskhelia, although Barcelona's interest is more concrete. There are management sources who confirm the Blaugrana's desire."