The 22-year-old only joined Chelsea from Borussia Dortmund for a total package worth £52 million in the summer of 2025.
Injury issues and a general lack of form meant he was unable to cement a regular place in the line-up under either Enzo Maresca or Liam Rosenior.
That seems to be the case now that Xabi Alonso is at the helm. Gittens has featured for just 55 minutes so far this season.
According to Corriere dello Sport, Gittens is expected to leave Chelsea in January, and Napoli are willing to offer him a way out.
Domestic rivals Roma reportedly came close to securing his services during the recent summer window, but Chelsea firmly rejected their opening €43 million bid.
Napoli are set to sell Noa Lang and Lorenzo Lucca to help fund a mid-season rebuild.