The Georgian winger grew up alongside Khvicha Kvaratskhelia at Dinamo Batumi, and the pair remain close friends who share the same agent, Mamuka Jugeli, according to TuttoSport.
Kvaratskhelia is said to have encouraged Kvernadze to try his luck in Italy in the first place, a piece of advice that is paying off handsomely for Frosinone.
The 23-year-old has scored three goals already this season for a Frosinone side sitting sixth in Serie A, building on the ten goals and assists he supplied last season as the club won promotion from Serie B. Frosinone paid only €300,000 to sign him permanently in June 2024, and TuttoSport reports his value has since multiplied roughly a hundredfold.
That rise has not gone unnoticed. Napoli sent a scout to watch Kvernadze in Frosinone's win over Como at the weekend, a move is seen as a natural step given his ties to Kvaratskhelia, who is said to hope he might one day face his friend in the Champions League.
Hull City are also alert to the situation in England, and could move as early as January, though Frosinone's position on any sale mid-season is unclear and unlikely to be straightforward.
For now, Kvernadze's focus remains on Frosinone's survival fight rather than any transfer, with his representative expected to take charge of weighing up his next step once that picture becomes clearer.