The South Korea international has been one of the many success stories for the Partenopei this term, playing an integral role in the Napoli Scudetto charge.
With Kim forming a formidable centre-back partnership with Amir Rrahmani, Napoli have opened up a 19-point lead at the top of the Serie A table and are on the verge of being crowned Italian champions for the first time since 1990.
The 26-year-old only joined Luciano Spalletti's side from Fenerbahce in the summer transfer window, and he has since posted two goals and an assist from 35 appearances across all tournaments for the Partenopei.
However, Kim only penned a three-year contract at Stadio Diego Armando Maradona - which will expire in 2025 - and a £42m release clause will reportedly be active for a couple of weeks in the summer.
Both Man United and Tottenham Hotspur are thought to be ready to battle for Kim's signature ahead of the 2023-24 season, and the centre-back was quizzed on the rumours while on international duty.
Kim had no time to discuss his future, though, and he implored the media to cease spreading such stories while he focuses on achieving success with Napoli.
"As you know, those rumours are not true at all. I want to focus on my team. I have many tournaments to play," the Daily Mail quotes Kim as saying.
"It's been four or years I have had these rumours. It's uncomfortable. I wish you don't spread those stories. I cannot be bothered by transfer rumours because they aren't true.
"Now I'm focusing on the team, rather than that kind of nonsense. There are so many important matches to go and right now I only want to focus on Napoli."
Despite Kim's comments, Napoli will likely be bracing themselves for offers for the 26-year-old in the summer, as Man United prepare to axe a wealth of their out-of-favour defenders.
Phil Jones and Axel Tuanzebe are seemingly guaranteed to head elsewhere this summer, while the futures of Harry Maguire and Victor Lindelof are also being called into question.
The pair have largely been consigned to the bench this season given the form of Raphael Varane and Lisandro Martinez, while Luke Shaw has also been utilised as a makeshift centre-half.
Lindelof has affirmed that he will wait until the end of the season before pondering his next career move, but the Red Devils are said to be willing to sell both the Swede and club captain Maguire.
Meanwhile, Varane has also revealed that he would be open to retiring at Real Madrid - having spent 10 years in the Spanish capital before moving to Old Trafford in 2021 - but the ex-France international is not expected to seek a move away from Old Trafford in the near future.