Kvaratskhelia has been the subject of transfer speculation in recent weeks and could make a move this January.
The winger has been linked with a move to Real Madrid and Paris Saint-Germain, as well as the Premier League.
Despite having a contract that expires in 2027, the Napoli star may depart the Serie A team this month.
Liverpool set sight on Kvara
Liverpool is reportedly one English team looking to sign Kvaratskhelia, according to The Athletic.
According to reports, the Reds are "alert" to Kvaratskhelia's predicament and "admirers" of him.
Liverpool will also have to compete with rumoured interest from teams like Chelsea and PSG.
The winger is reportedly valued at £67 million in Italy, so a move for him would be much more expensive.
Meanwhile, this season, Kvaratskhelia has contributed three assists and five goals in Serie A.
His efforts have enabled the team to contend for the top spot in the Italian Serie A League.