Zaha, 20, was an Arsenal fan as a youngster and Wenger is hoping that can persuade the winger to join the Gunners rather than Manchester City who would undoubtedly have the financial advantage.
He has impressed so far this season for Crystal Palace and also earned his first senior England call up, but his manager Ian Holloway would be reluctant to let him go in the winter transfer window.
“It would be easy to cash in on Wilfried in January, but the feeling at the club is that it would be a false economy. It is a case of giving it our best shot to win promotion and that means keeping Wilfried at Selhurst Park,” Holloway told The Sunday Mirror.
A move at the end of the season would seem more likely but Wenger, in a bid to fight off competition from other clubs could look to a deal where Zaha is signed in January and loaned back to Palace until the end of the season.