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."