A section of West Ham's support was reported to have mocked the gassing of Jews in the Holocaust and chanted about Nazi dictator Adolf Hitler during the London derby, which Tottenham won 3-1.
Tottenham have a significant fanbase in the Jewish community and an FA spokesman said it was "likely" that the governing body would launch a formal investigation once the match officials' reports had been received.
The incident came just days after a Tottenham fan was stabbed before a Europa League game against Lazio in Rome in an apparently anti-Semitic attack by Italian hooligans.
West Ham supporters also sang "Viva Lazio", "Can we stab you every week?" and hissed on several occasions, mocking the mass execution of Jews during World War II.
The east London club responded to the potential FA investigation by pledging to hand out life bans to any fans found found guilty of anti-Semitic chants.
"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," the club said.
"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," a statement read.
"During the 46 games in the Championship (second division) 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 also been reported to the police by a campaign group.
Peter Herbert, chairman of the Society of Black Lawyers, confirmed that his organisation had contacted London's Metropolitan Police to complain about the West Ham supporters' actions.
Asked if he would take the issue to the police, Herbert told Sky Sports News: "We've done so already.
"In fact, we were due to meet a borough commander of the Met Police either later this week or early next week, and it's one of the things that will be on our agenda.
"As far as we're concerned, there has to be zero tolerance of this. If these people can be identified on camera and prosecuted, then that is something we'd like to see happen."
It was a complaint from Herbert that prompted police to investigate an allegation of racial abuse made against referee Mark Clattenburg by Chelsea last month.
The police subsequently dropped their investigation due to a lack of evidence, while Clattenburg was cleared by the FA.