West Ham are working with West Brom and Jake Livermore to discover what sparked the England midfielder's altercation with home fans at the London Stadium.
Livermore, who was substituted just after the hour, had to be escorted down the tunnel following the incident.
Neither West Ham nor West Brom would comment on a Sky Sports News report today morning that Livermore had reacted to a home fan shouting about his baby son, who died in 2014.
West Brom boss Alan Pardew said after his team's 2-1 defeat that he had seen Livermore among supporters in the crowd but did not know what had provoked his actions.
It is understood the London club are actively looking into the matter, working with Tuesday night's visitors and 28-year-old Livermore to uncover what exactly the alleged abuse was.
Speaking after the match, Pardew said: "The only thing I know is I see Jake in the crowd, which disturbed me. Obviously you don't want to see a player in the crowd.
Was right next to the Livermore incident. Here he is being taken away... pic.twitter.com/rhTmI44dsF— x (@ironswhufc66) January 2, 2018
"There's no way he's going in the crowd - because I know him, he's a great lad - unless he was provoked severely. That's all I know.
"I haven't had a chance to talk to Jake. I'll speak to Jake and we'll go from there."