While Manchester United are said to be the keenest to snap up the South Korean international, it is believed that both the Blues and Manchester City are also fans of the 6ft 3 defender.
Kim only made the switch to Italy for €18m last summer, but he has played a key role in helping Napoli win their first Serie A title in thirty years.
The 26-year-old performances have clearly attracted the attention of Premier League scouts and the existence of a buyout fee is likely to tempt teams into making an offer.
Kim’s contract includes a clause that means he can leave Napoli for €60m (£53m) between July 1st and July 15th, so it is a small window of opportunity for Chelsea to get a deal done.
Whether the London club will make an approach for the centre-half, it remains to be seen. They are not exactly short of defenders as it is, with the likes of Wesley Fofana, Thiago Silva, Benoit Badiashile, Kalidou Koulibaly and Trevoh Chalobah in the first-team squad. Levi Colwill will also return from his loan spell at Brighton this summer.