Television cameras picked up Wilshere raising his middle finger in the direction of home supporters at the Etihad Stadium during the second half of the Gunners' 6-3 defeat on Saturday.
Although the incident was missed at the time by referee Martin Atkinson and his officials, the FA were able to retrospectively implement disciplinary proceedings against the player under a new pilot scheme for 'not seen' incidents in Premier League matches.
As such, an independent three-man panel agreed if the gesture had been viewed during the game, then it would have merited a dismissal.
However, with the precedent of a two-match suspension handed out to Blackpool winger Tom Ince when he retrospectively charged in relation to a gesture towards a match official in a Capital One Cup tie against Preston earlier this season, Press Association Sport understands Arsenal have submitted mitigating circumstances to the governing body, arguing the length of the punishment is excessive.
In December 2011, Liverpool striker Luis Suarez was suspended for one match, fined £20,000 and warned as to his future conduct after he made a gesture to home fans as he walked off the pitch following a 1-0 defeat at Fulham.
An FA disciplinary commission will now consider Wilshere's case when it meets on Thursday, and make a definitive ruling.
If the two-match suspension is upheld, then the England international would miss the showdown with Chelsea at Emirates Stadium on December 23 and also the Boxing Day fixture at West Ham.