The Hammers are unhappy that the England striker's ban - a consequence of being sent off against Swansea last week - was not overturned.
Co-owner David Gold said on Thursday that his club were seeking "legal redress" over the matter, although a statement on West Ham's official website this morning ruled out any sort of court action.
"West Ham United are today (Friday) appearing before an FA Arbitral Tribunal in a challenge to the FA Regulatory Commission's decision relating to the three-match suspension of Andy Carroll," it read.
"The club is concerned that the Regulatory Commission did not apply the correct test under the rule, and denied the club procedural fairness.
"West Ham's complaint is made under the FA Rules, and the club shall accept and abide by the decision of the FA Arbitral Tribunal.
"The club has no intention of taking the issue to the courts, but simply seeks a fair determination of its rights under the FA's Rules."
Referee Howard Webb made the decision to send off the striker after a clash with Swansea's Chico Flores.
Carroll is now facing a three-match ban and Gold said that could mean the difference between relegation and top-flight survival.
Gold told Press Association Sport on Thursday: "We are hugely disappointed at the outcome of the process.
"There is nowhere to go other than to seek some kind of legal redress. It's not ideal, the last thing I want to do is go to some kind of legal issue because I think it is a footballing issue.
"But we are fighting for our lives. If we were mid-table we would probably get on with it but we are fighting for our lives to retain our Premier League status and we owe it to our fans, we owe it to ourselves."
Hammers manager Sam Allardyce said at his Friday morning press conference: "My reaction to Andy's red card was one of injustice. Unfortunately the panel has not seen it as they should have.
"In this case we based our procedure on whether it was an obvious mistake (to send him off) and I'm 100 per cent certain it was an obvious mistake.
"I hope that common sense prevails. If there's a decision today hopefully it's a positive one."