ESPN reports that the midfielder could face action from the Football Association after television cameras appeared to catch him raising a finger to home supporters at the Etihad Stadium.
The Gunners manager said: "I didn't see that. I don't know if he did it. If he did it and is banned, we will have to accept it."
The governing body will decide whether Wilshere should be punished for the incident once they receive referee Martin Atkinson's match report.