The Hammers are furious after their appeal over the red card – issued by World Cup referee Howard Webb – was dismissed on Tuesday.
They now want the FA to agree to an arbitration hearing under Rule K, which would see an independent body judge on the dispute.
If they do not get one, the Hammers are set to go to the High Court to seek an injunction to block Carroll’s dismissal and subsequent ban, pending a personal hearing.
That would free up the former Liverpool striker to play in the crucial relegation clashes with Aston Villa on Saturday, and Norwich next Tuesday.
However, the unprecedented action from the Hammers is set to have big ramifications.
All Premier League clubs have signed up to an FA agreement that the final decision of an independent panel in relation to wrongful dismissal is not subject to appeal.
The Hammers have enlisted tip QC Lord David Pannick to help with the case, and he has queried the FA’s claim that there has to be an ‘obvious error.’
Their statement on Tuesday said: “As stated in the Rules and Regulations of The FA, an Independent Regulatory Commission must apply the test of whether the decision to dismiss a player was ‘an obvious error.’”