The Serb arrived from Torino last year on loan, but he was confined to the bench for the majority of the 2016/17 season and made just 12 appearances.
Despite that, Napoli were obliged to make his deal permanent in the summer and did so for €25 million (£22.4 million). The centre-back's situation is yet to improve, however, and he has featured just twice for the Partenopei this season.
The Gunners could use more reinforcements in defence, particularly in light of Shkodran Mustafi's injury suffered on international duty on Sunday.
Germany manager Joachim Low believes he could face a lengthy lay-off, per Goal:
That's where Maksimovic, 25, could come in.
He has had little chance to showcase his talents in Naples, but he impressed football journalist David Amoyal while at Torino:
The defender also showed himself to be a strong reader of the game, as demonstrated by WhoScored.com:
He could be a slightly risky proposition, given he has played little football in the last 12 months. And while Napoli appear to have little use for him, it's likely they will want to recoup as much as they can on him.
Nevertheless, Maksimovic is a talented player who could get back to his best if given the opportunity to kickstart his career.
He would most likely jump at the chance to play regular football once again, though Inter may also prove a tempting option if he would prefer to remain in Italy.