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 is 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.
At the first league match at the venue - against Bournemouth last month - some fans arrived with tickets for seats that did not exist, while fighting broke out between rival supporters outside the stadium.
Some of the disturbances are believed to be over persistent standing during matches, with some fans ejected at the Watford match, which West Ham lost 4-2.
Before the game, West Ham co-chairman David Gold tweeted that the club was "trying to achieve harmony" between fans who want to sit and those who wanted "to stand and increase [the stadium's capacity] to 66,000".
On Sunday he wrote: "I want to assure everyone that the club is working flat out to solve the sitting/standing issue."