West Brom have said Jake Livermore confronted a West Ham fan at London Stadium after a comment was made about the death of the player's infant son, reports BBC Sport.
The midfielder was involved in an angry exchange after he was substituted in the second half of his side's 2-1 loss.
Livermore and his partner lost their newborn son Jake Junior in May 2014.
West Brom have offered their "total support" to the England international and have sent their observations to the Football Association.