On the mobile phone footage, which was shared on social media, a supporter in the West Ham end can be heard directing expletives towards Salah and abusing the Egypt international on the grounds of his Muslim faith.
A statement from West Ham read: "At West Ham United, we have a zero-tolerance policy to any form of violent or abusive behaviour.
"We are an inclusive football club. Regardless of age, race, religion or belief, marriage or civil partnership, pregnancy or maternity, sex, sexual orientation, gender reassignment or disability, everyone is warmly welcomed at London Stadium.
"Anyone identified committing an offence will have their details passed to the police and will face a lifetime ban from London Stadium. There is no place for this kind of behaviour at our stadium."
Omnisport understands the police are aware of the incident, while anti-discrimination campaign group Kick It Out have also sought further information.
West Ham and Liverpool played out a 1-1 draw, with Michail Antonio cancelling out Sadio Mane's opener for Jurgen Klopp's side before half-time.