The 22-year-old joined Napoli from Georgian club Dinamo Batumi for a €12m (£10.5m) fee last summer, and he has quickly established himself as an integral part of Luciano Spaletti's side.
Kvaratskhelia has scored 10 goals and provided 11 assists in 19 league appearances this season, helping Napoli establish a 15-point gap at the top of the Serie A table.
The Georgia international has also registered two goals and four assists in the Champions League after he set up Giovanni Di Lorenzo's goal in Tuesday's 2-0 win over Eintracht Frankfurt in the first leg of their last-16 tie.
Although Kvaratskhelia has a contract with Napoli until June 2027, he is already being linked with a move away from the Stadio Diego Armando Maradona.
Real Madrid, Paris Saint-Germain and Manchester City are among those who are showing an interest in the Napoli star.
However, Napoli director Cristiano Giuntoli has stated that the Italian club are not prepared to sell Kvaratskhelia.
"Khvicha's a fantastic player and we want to keep him," Giuntoli said. "It is not even the case to mention a specific price tag to sell him.
"In this moment, Kvaratskhelia is not for sale. The market hasn't even started."
The player's agent Mamuka Jugeli also recently claimed that Kvaratskhelia is focused on winning Napoli's first Serie A title since the 1989-90 season.
Jugeli told CalcioNapoli: "There is a lot of interest from other clubs. Kvara, however, is only thinking about winning the Scudetto and Napoli's matches in the Champions League.
"He loves being [for Napoli]. He told me that in terms of football in Italy, he sees himself only in Naples. He will never play for any other Italian club, apart from Napoli. He feels in Naples as at home."
With several European giants circling Kvaratskhelia, Napoli are taking steps to prevent a departure in the near future.
They are reportedly set to offer the winger an improved contract, which would result in a significant pay rise.
Kvaratskhelia will be hoping to help his side claim a seventh straight competitive victory when they face Empoli on Saturday.