The 21-year-old joined Napoli from Dinamo Batumi in July, and he has been in impressive form for the Italian side this season, scoring seven goals and registering eight assists in 14 appearances.
Kvaratskhelia has managed five goals and five assists in 10 Serie A appearances, while he has scored twice and provided three assists in four Champions League outings.
The Georgia international has a contract at Napoli until June 2027, but his early-season form has allegedly attracted the interest of some of the biggest clubs in European football.
According to 90min, Real Madrid, PSG and Man City have all sent scouts to watch the attacker this season with the view to potentially moving for him next summer.
However, the report claims that Napoli are not prepared to let the winger leave next year under any circumstances, and the Italian outfit could even offer him a new and improved contract.
In a recent interview with Georgia's edition of Sport, Kvaratskhelia revealed that he "dreamed" of playing for Real Madrid when he was a youngster, but the forward is delighted to be at Napoli.
"I dreamed of playing for a big club growing up, that was Real Madrid, but Napoli is a big club - my dream has already come true," he said.
Meanwhile, when asked about his future, Kvaratskhelia said that he could not predict what would happen.
"I am not sure, let's see what happens," he added.
Kvaratskhelia started his professional career with Dinamo Tbilisi before joining Rustavi, spending a period out on loan with Lokomotiv Moscow during his time at the club.
The forward then represented Rubin Kazan between 2019 and 2022, leaving the club earlier this year following Russia's invasion of Ukraine.
Kvaratskhelia has starred in the Champions League this season, providing a goal and an assist home and away against Ajax in Napoli's two most recent fixtures in the competition.
Luciano Spalletti's side have already qualified for the knockout round of the European Cup with two games to spare, while they sit at the top of Serie A, boasting 26 points from their opening 10 games of the season.