West Ham intend to impose life bans on any fans found guilty of anti-Semitic chants during the 3-1 defeat at Spurs on Sunday.
The FA says it is "highly likely" to launch an investigation into reports of abuse aimed at Tottenham fans.
An FA spokesman said reports from match officials and delegates would be assessed before any action was decided on.
West Ham's statement read: "West Ham United are in contact with Tottenham Hotspur to assist them with their investigation into the conduct of a small number of supporters and alleged inappropriate chanting during yesterday's match at White Hart Lane.
"West Ham United will take the strongest possible action against any of their supporters, including enforcing life bans from the club, that are found guilty of behaviour which is categorically not condoned by West Ham United.
"During the 46 games in the Championship last season, West Ham United had zero arrests for racism or violence, so while we are surprised to see such reports today, we will examine any available evidence of such conduct thoroughly and take the appropriate action."
The matter has been reported to the police, the chairman of the Society of Black Lawyers Peter Herbert told Sky Sports News.