The 23-year-old has been a revelation for the Partenopei since making the switch from Georgian giants Dinamo Batumi during the summer transfer window of 2022.
Kvaratskhelia enjoyed a productive term in Serie A this season despite his side being unable to retain their Italian crown, finding the net on 11 occasions in 34 appearances.
The attacker's debut term in Naples put him on the radar of a host of top European clubs, when the full international bagged 14 goals and provided 14 assists across all competitions.
As well as for Napoli, Kvaratskhelia is also a star man for his national side, earning 30 caps for Georgia since making his international debut in 2019.
Barcelona, PSG have Kvaratskhelia dreams dented?
According to Gazzetta dello Sport, both Barcelona and PSG have been dealt a major blow in the pursuit of Kvaratskhelia ahead of this summer's transfer window.
The report states that Napoli are close to agreeing a deal for a new contract with the 23-year-old, who looks set to stay in Naples for at least another year.
It is understood that the fresh agreement will contain a release clause, meaning that the 2022-23 Italian champions are protected from losing the attacker for cheap.
Under the leadership of Antonio Conte, Napoli will be looking to fight for the Scudetto next campaign, with a key being their ability to retain star players.
With leading marksman Victor Osimhen being linked to Premier League clubs such as Arsenal, it is believed that Napoli are not willing to lose both the Nigerian and Kvaratskhelia this summer.
Post-Kylian Mbappe problems
Already a transfer saga which has seemingly lasted for half a decade, PSG's all-time leading goalscorer Kylian Mbappe has sealed a move away to Real Madrid.
Harnessing the backing of Les Parisiens' hierarchy and passionate supporters, Luis Enrique is now tasked with delivering domestic and continental success to the French capital without one of the greatest players to ever grace the country.
Scoring 44 goals across all competitions last term, Mbappe's departure leaves a massive chasm in goal contributions to fill during the summer trading point.
With news of Kvaratskhelia preparing to stay put at Napoli, PSG will be required to search elsewhere as they attempt to replace the club's biggest-ever star.