The East London club said in a statement on Monday that they were working with Tottenham to identify fans who could be heard taunting Spurs supporters, who have strong Jewish ties.
West Ham fans are alleged to have sung "Viva Lazio" and "Can we stab you every week?" in relation to the attack which left a Tottenham fan seriously injured when a group stormed a bar Spurs supporters were drinking at in Rome ahead of a Europa League match with Lazio last week.
Media reports also said fans chanted "Adolf Hitler, he's coming for you" and hissed, mimicking the gassing of Jews during the Holocaust.
"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 statement 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.
"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."
Promoted West Ham's manager Sam Allardyce told reporters he did not hear any controversial chanting by away fans.
"I don't hear what the fans say or do when I'm concentrating as a manager on a game of football," he said.
"They shouldn't be doing things like that, it is the least of my worries at the minute isn't it? What do you want me to say? If I didn't hear it I can't condemn it can I?"
