West Ham will continue "a full investigation" into the incident at the London Stadium which saw West Brom midfielder Jake Livermore move to confront a fan who allegedly made a comment about the death of his baby son.
England international Livermore, who was substituted just after the hour during Tuesday's Premier League match, had to be escorted down the tunnel following the incident, which was not clearly picked up on CCTV footage.
West Brom issued a statement on Wednesday afternoon saying their player had been "subjected to general abuse from home supporters which he shrugged off," but also that Livermore acknowledged "he moved to confront one spectator who chose to make a comment about the death of his infant son."
West Ham acted quickly to eject the fan and are working with West Brom to determine whether the abuse directed was about the player's baby son, who died in 2014.
The Football Association has also requested observations from all parties, which must be received by 6pm on Thursday.
Once the investigations are concluded, West Ham intend to take "appropriate action", with a stadium ban being considered.
"West Ham United can confirm that the individual involved in an altercation with Jake Livermore during last night's match against West Bromwich Albion was immediately identified and removed from London Stadium," a club spokesman said.
"After the game concluded, West Ham officials liaised with West Bromwich Albion, Jake Livermore himself and the Metropolitan Police to commence a full investigation into the incident.
"The player has today confirmed he does not wish to make this a police matter.
"However, given the nature of the allegations, the club will continue to investigate before taking the appropriate action."
West Brom, meanwhile, have offered the "total support of everyone at the club" to Livermore.
"The club would like to think that all right-minded football supporters could understand this reaction which did not result in any physical exchanges before Jake was led away to our dressing room," the statement added.
"Jake is an outstanding young individual who has the total support of everyone at the club and he has made it clear he considers this statement to be an end to an unhappy incident."
West Ham were also praised for the way the matter was handled at the time, with West Brom "more than happy to leave any further action they deem appropriate in their hands", adding they had responded to the FA's request for observations, but would not be making any further comment.
Livermore joined West Brom from Hull on a four-and-a-half-year deal in January 2017 in a reported £10million move.
The former Tottenham midfielder tested positive for cocaine after Hull's Premier League win over Crystal Palace in April 2015 and played three further matches before being banned by the FA.
Livermore, though, subsequently escaped a further suspension after the FA ruled the death of his new-born son during May 2014 was an overwhelming mitigating factor.
The midfielder was, however, ordered to undertake a course of rehabilitation and education, and was also the subject of target testing for a period of 12 months.