The 24-year-old is facing an uncertain future at Stamford Bridge having failed to establish himself as a first-team regular under head coach Mauricio Pochettino.
Chalobah featured regularly for the Blues in pre-season, but injuries and the addition of new signings in the summer transfer window have resulted in the defender falling down the pecking order in West London.
The academy graduate has made a total of 63 appearances for Chelsea in all competitions since and including his debut in 2021, including 34 outings last season, but is yet to make a single appearance in the current campaign.
Axel Disasi, Thiago Silva and Levi Colwill have all featured regularly in defence this term, while Benoit Badiashile and Wesley Fofana, the latter remains sidelined with a knee injury, are both believed to be in Pochettino's long-term plans.
A recent report claims that Chelsea are unlikely to attract suitable bids for Chalobah in January as the defender is not close to returning to full fitness.
However, according to Tuttomercatoweb, Serie A champions Napoli have identified the Englishman as a potential target this month.
The report adds that Napoli are keen to strengthen their squad in a number of positions during the January transfer window, with additions in defence a priority for manager Walter Mazzarri.
Chalobah's older brother Nathaniel Chalobah briefly joined Napoli from Chelsea on loan for the 2015-16 season, but he made just nine first-team appearances and now plies his trade at West Bromwich Albion.
Napoli are understood to have a number of other defensive players on their shortlist, including Udinese's Nehuen Perez, Rennes' Arthur Theate and Brest's Lilian Brassier.
Previous reports have claimed that Bayern Munich and Borussia Dortmund held an interest in Chalobah, but both clubs have seemingly switched their attention to other targets, with the former recently signing Eric Dier from Tottenham Hotspur.
Italian outfit Roma, managed by former Chelsea boss Jose Mourinho, have also been linked with Chalobah, who is under contract at Stamford Bridge until the summer of 2028.
The prospect of remaining in the Premier League has also been mooted for Chalobah, as the likes of West Ham United, Tottenham, Crystal Palace and Nottingham Forest have all been credited with an interest in the defender.