According to the Daily Mail, the Frenchman has finally caved in to pressure from fans and club shareholders to sign the Uruguay international in order to improve the Gunners' season.
Arsenal's 3-3 draw with Fulham at the Emirates on Saturday saw them fall 11 points behind Premier League leaders Manchester United.
Wenger had sent chief scout Steve Rowley to Naples to watch Cavani against Dnipro Dnipropetrovsk in the Europa League on Thursday, and got a favourable report following the 25-year-old's four goals for the Azzurri in their 4-2 victory.
Cavani, though, has maintained that he does not plan to leave Napoli anytime soon. His current contract with the former Italian champions lasts until June 2017.