TV Footage on the internet showed United's Fellaini standing over Zabaleta during the 3-0 defeat at Old Trafford.
The video suggested Fellaini spat at the Manchester City defender.
The FA feels there is insufficient evidence from that posting to see if there is something to warrant a charge and is trying to find out if there are any clearer images of the incident.
Should such evidence be forthcoming, the FA would then need to decide whether to charge the Manchester United midfielder.
Last week, Hull forward George Boyd was suspended for three games after being found guilty of spitting at Manchester City keeper Joe Hart.
Prior to the alleged spit, Fellaini caught Zabaleta in the face with his forearm. Fellaini was booked for the clash, although many observers believed the incident deserved a red card.
Fellaini has made 10 appearances since his move to Old Trafford in September from Everton.