Carroll was shown a straight red card by referee Howard Webb following an altercation with Swansea defender Chico Flores.
The Upton Park club had until 1pm on Monday to inform the FA of their intention to challenge the dismissal and now have a further 24 hours to collate and submit their evidence.
A three-person independent panel will be convened to assess written evidence from the match officials and the Hammers, as well as footage of the incident.
A three-match suspension would rule Carroll out for the rest of February and would see him miss matches with Aston Villa, Norwich and Southampton.
The 25-year-old made just his third start of the season following a heel injury and set up both goals for Kevin Nolan in the 2-0 victory.
Hammers manager Sam Allardyce declared his intention to contest Carroll's dismissal after the match and was critical of Flores.
Allardyce said: "We will hope that the appeal will work. Hopefully we don't lose Andy for three games.
"He's gutted. He's absolutely beside himself. We'll just have to go through the process and see what happens."
Howard webb and the FA are hand in clove with each other ,a good ref but one that thinks he,s right every time and the F A will back him on this,NO way should that of been a red,andy carrol didnt know that cheating actor was behind him ,unless he,s had the operation to add a couple of eyes to the back of his head,may be a yellow for his arms swinging but the other guy should get an oscar for his play acting,i hate this side of football the diving and acting to cheat others its about time refs could have a look at the game after and add cards where they have missed them ,,- steviebhoy1888