The 26-year-old centre-back joined Napoli last summer and has been one of the most impressive defenders in Serie A this season.
His performances have formed the backbone of an impressive Napoli side who are considered by many to be the best side in Europe this term.
However, Napoli are facing the threat of losing him next summer due to interest from some of the biggest clubs in Europe.
Kim is on Manchester United’s radar as the Erik ten Hag looks to add one more centre-back to his squad, but according to Italian daily Corriere dello Sport, Napoli are already working to keep him at the club.
The Serie A leaders are pushing Kim to sign a new contract on improved terms in line with his performances.
His €48m release clause is also a problem for Napoli next summer and the club are trying to solve that through a potential new deal.
If he agrees to sign a new contract, the release clause is likely to go up to €65m from the current figure.
The Serie A giants do not want to lose Kim after just one season and are hoping to convince him to sign a new deal soon.