The Hammers on Monday formally notified the FA of their intention to appeal against Carroll's dismissal for an altercation with Swansea defender Chico Flores and now have until 1pm on Tuesday to submit evidence in their bid to have his automatic suspension overturned.
An independent three-person panel is poised to hear the case on Tuesday afternoon, with their judgement expected later in the day.
Carroll was shown a straight red card by referee Howard Webb in the second half of the Hammers' 2-0 win and video footage of the incident, as well as written evidence from the Hammers and match officials, will be assessed.
A three-match suspension would rule Carroll out for the rest of February and 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 in midweek.
"All I can hope is that the panel, in the cold light of day, see it for what it is.
"He (Webb) can't be absolutely certain of what's happened, except that Chico Flores is over-exaggerating, which is generally the norm for him, unfortunately."