Livermore became embroiled in a row with a spectator after being substituted in West Brom's 2-1 defeat at the London Stadium last week.
Livermore has been reminded of his responsibilities as a player, however, and was cautioned over going into crowds to ensure his safety and that of supporters.
In the aftermath of the incident, West Brom confirmed that the England worldwide reacted by entering the stands "to confront one spectator who chose to make a comment about the death of his infant son".
West Ham have also promised to deal with the fan in question and will take action where appropriate, with the east London club confirming that they have identified the individual and that he was spoken to by staff at the stadium and removed during the match.
Livermore clashed with the West Ham fan immediately after being taken off at London Stadium
Having asked both clubs for their observations, the FA is understood...
West Ham said in a statement earlier this month that they would issue a life ban to the supporter who abused Livermore.
West Brom and England midfielder Livermore has, however, been gently reminded by the game's disciplinary that he can not take the law into his own hands.
A year later the midfielder tested positive for cocaine, but escaped a ban because of "the unique nature of the circumstances" involved.
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