The newly-monied Premier League side are set to continue investing after their superb start to the season, with Kvaratskhelia at the top of their list, according to The Times.
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The 21-year-old winger has thrilled fans in Italy and Europe with his trickery off the touchline, already becoming a cult hero in Naples.
The Georgian has earned the nickname 'Kvaradona' in reference to club legend Diego Maradona, with his dribbling and playmaking catching the eye of a number of clubs.
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Particularly Eddie Howe's Magpies, with The Times claiming Kvaratskhelia has been heavily scouted in the lead up to the World Cup, and character checks have been made.
The outlet also names Real Madrid and Paris Saint-Germain as suitors, but Newcastle's financial might and determination suggests they're ready to fight.
Kvaratskhelia only joined Napoli in the summer from Georgian side Dinamo Batumi for £10m, but it could take at least five-times that fee to dislodge him from his contract that runs until 2027.
No player in Serie A has more goal contributions than the wingers 11, with his six goals and five assists helping the Italian giants to a mighty impressive 13 wins and two draws from their opening 15 league games.
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Kvaratskhelia has also starred in Europe, having helped Napoli top their Champions League group ahead of Liverpool, with the Georgian managing two goals and three assists, one of which came in a 4-1 thumping of the Reds.
Newcastle have invested heavily since they were taken over by Saudi Arabia's Public Investment Fund in October last year, and have been widely regarded as wise spenders with a number of shrewd purchases.
It's understood that Napoli are already keen to tie Kvaratskhelia down to new terms beyond his current contract, but that's unlikely to deter Newcastle who could field a terrifying front line that includes club record £60m man Alexander Isak and Allan Saint-Maximin.
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The Magpies sit third in the Premier League after an impressive start to the season and resume their campaign as England's form team with a League Cup tie against Howe's old side Bournemouth on December 20.