He is set to become Arsenal's youngest captain of all time at Brighton today.
Wenger said: "At the moment, for me, we have two captains - Vermaelen and Arteta - and after that, occasional captains.
"On the day, why not? He can be, yes."
Wenger may yet decide to rest the midfielder, but should he hand Wilshere the armband it will see him beat the club record held by Tony Adams.
Aged just 21 years and 25 days, Wilshere would eclipse legendary defender Adams' mark by 57 days.