The Football Association will assess reports of crowd trouble at West Ham's match with Watford on Saturday before deciding if further action is required.
The FA are also expected to contact the Hammers about the events in the stands at their new London Stadium home.
West Ham promised a "zero tolerance" approach to any fans found guilty and said they would be banned for life.
"We will request courts serve banning orders to prevent these individuals attending any football," the club said.
West Ham's first season at the London Stadium in Stratford, formerly the Olympic Stadium, has been marred by unsavoury incidents involving their fans at the last three matches, with criticisms being made over stewarding and segregation arrangements.