The Egypt international was filmed on a mobile phone from a section of home supporters as he was taking a corner.
A male can be heard shouting: “Salah you f****** Muslim. F****** Muslim c***. F*** off”.
The user who posted the video on Twitter said: “I was disgusted by what I was hearing. People like this deserve no place in our society let alone football matches. #kickracismout”
A West Ham spokesperson said the club has “a zero tolerance policy to any form of violent or abusive behaviour” and is taking immediate action to identify the individual or individuals concerned
The statement added: “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.
“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.”
The Metropolitan Police are also reviewing the footage as enquiries continue.
"We are aware of a video in which it appears racial abuse is being directed at a player at a West Ham vs Liverpool game at London Stadium on Monday, 4 February," a statement from the Metropolitan Police said.
"Officers are in the process of reviewing the footage. No arrests have been made and enquiries continue.
"Anyone who witnesses inappropriate behaviour during a match is urged to bring it to the attention of a steward or police officer."
Kick It Out, football's equality and inclusion organisation, offered their support to the investigations.
"We are dismayed to see yet another high-profile incident of discrimination in English football - this time a video of disgraceful anti-Muslim abuse aimed at Liverpool's Mohamed Salah by a West Ham United supporter," the anti-discrimination campaign group said in a statement to Press Association Sport.
"We have informed the club, the FA and the UK Football Policing Unit and have offered our support to the investigation, which is already under way.
"We are pleased that West Ham officials have expressed their determination to identify the supporter and take firm action - this type of behaviour is simply unacceptable and must be challenged swiftly and decisively."
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