The Gunners tried to sign the 24-year-old last summer, but failed in their endeavours. Instead the forward joined the Old Lady from Sassuolo, with the Serie A champions having an option to buy him ahead of other sides.
However, despite only signing the Italy international in July, the Bianconeri are already happy with selling the player. The striker is apparently not the type of player manager Massimiliano Allegri wants in Turin.
The former AC Milan boss also signed Mario Mandzukic and Paulo Dybala in the last transfer window, and the pair will likely be used ahead of Zaza. Alvaro Morata is also still at the club, meaning that the Arsenal target could be surplus to requirements for the Champions League finalists.
The Gunners look in need of a forward, having only hit the back of the net once this season with it not being an own goal. Olivier Giroud and Theo Walcott have been out of form, and Danny Welbeck is injured for the foreseeable future.