The Georgian, who has been compared to Argentina legend Diego Maradona, has become one of Serie A's best attackers after joining Napoli from Dinamo Batumi in the summer of 2022.
In his first season in Italy, Kvaratskhelia scored 12 goals and provided 13 assists in 34 league matches to help Napoli end their 33-year wait for the Scudetto.
Kvaratskhelia was unable to match those numbers in what proved to be a disappointing 2023-24 campaign for Napoli, but he still managed to register 19 goal contributions in 34 Serie A outings.
Despite having a contract until 2027, Kvaratskhelia's future is drawing significant speculation, especially after his father admitted he wants his son to leave the Italian club.
Liverpool make Kvaratskhelia enquiry
The player's agent and father Mamuka Jugeli recently told Imedi: "I don't want my son to stay at Napoli. They changed three coaches last season, and it's hard to play in a similar situation."
In response, Napoli released a statement to reinforce the fact that Kvaratskhelia still has three years left to run on his contract, and they are not open to a summer sale.
While Napoli are keen to keep Kvaratskhelia, Liverpool are said to be among the clubs considering a potential summer move.
According to Caught Offside, the Reds have made an enquiry to establish Napoli's asking price and the player's wage demands.
The report suggests that Liverpool are readying to pounce if it becomes clear that the Georgia international could leave Napoli during the course of the transfer window.
Kvaratskhelia to decide future after Euro 2024
French champions are also interested in signing Kvaratskhelia as they look to replace the void left by France star Kylian Mbappe.
There is also a possibility that Kvaratskhelia could still reach an agreement to extend his contract with Napoli.
However, he has revealed that he will put any decisions over his future until he has finished representing his country at Euro 2024.
"I'm fine, I'm only focused on the national team," he told Sky Italy."After the European Championships, I will decide my future.
"Now I don't think about it, I just want to give everything I have on the pitch to help my national team. I don't think about what they say, I'm 100% focused only on Georgia."
After losing to Turkey in their tournament opener, Georgia will be looking for a response when they face the Czech Republic on Saturday.