The report claims that Arsenal have been scouting Maksimovic, presumably on international duty, and are tempted to make a move in January.
Arsenal are not alone in their pursuit of the defender, though, as Italian side Inter Milan are also said to be monitoring his progress.
Maksimovic could be free to leave Napoli in January, due to his bit-part involvement so far this season.
He has made two appearances in all competitions so far, and struggled to retain a regular place in the side last season.
The Serbian joined the club from Torino for €25m last summer but has failed to live up to his price tag as of yet.
Arsenal will be hoping that they can secure a deal and bring out the best in the tall defender, if they can beat Inter to the punch.