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 on Wednesday 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.
Speaking after the match, Pardew said: