Cole was dismissed by referee Anthony Taylor for a high challenge on Leighton Baines in the second half as the Hammers were beaten 2-1 by Everton at Upton Park.
West Ham next travel to Reading on December 29, with the hearing set for Cole's appeal scheduled for two days earlier.
Everton have also submitted an appeal into Darron Gibson's red card which was shown after he collided with Mark Noble in stoppage time during the same game.
The paperwork needed to be submitted to the FA by 1pm today but the appeal means Gibson will be able to play in the Boxing Day match against Wigan Athletic, with his case also due to be heard on December 27.
- Sports & Recreation
- Darron Gibson
- Leighton Baines