The 21-year-old has starred for the Serie A table-toppers since arriving in the summer from Dinamo Batumi for £10million.
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Kvaratskhelia linked up with Dinamo from Rubin Kazan earlier this year with Russia's invasion of Ukraine allowing foreign players to suspend their contracts.
His talent was there for all to see when he destroyed Liverpool in Napoli's 4-1 Champions League group stage victory last month.
In 14 games in all competitions this term, the Georgian winger has chipped in with seven goals and eight assists.
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The youngster has been dubbed as the 'new Georgi Kinkladze' due to similarities between their pace and dribbling.
And he could follow in the footsteps of his compatriot in joining the Citizens with boss Pep Guardiola identifying him as a serious target.
That is according to SunSport, who have declared that City are keeping tabs on the 19-cap international.
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It's not just City that are interested in the forward, with Real Madrid and Paris Saint-Germain also admirers of him.
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But it has been said that it is City that Kvaratskhelia would be more inclined to join due to Kinkladze's spell at the club in the 1990s.
Napoli are aware of the growing interest in him and are already looking to hand Kvaratskhelia fresh terms despite tying him down to a five-year deal.
The Italian outfit want to insert a £65m buyout clause in his contract where they would bank a healthy £55m profit.
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But Kvaratskhelia is claimed to be reluctant to sign a new deal as he wants to weigh up his options after three months in Naples.
His Napoli teammate Victor Osimhen believes the wide man can help fire his side to a first Scudetto title since 1990.
He told DAZN: "I am really happy for him, he deserves everything he is getting now. He is just getting started, you guys have seen nothing yet.
"I believe he has the quality to make us dream this season, he has big confidence and we are here to help support him.
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"You can see he has been decisive for us."