Away supporters referenced Spurs' recent trip to Lazio in which 10 fans were injured along with singing other deeply offensive songs, according to witnesses at White Hart Lane
"We're investigating the matter and we'll speak to both clubs today," an FA spokesperson told Goal.com.
Sections of the Hammers’ away contingent were heard making anti-Semitic chants mentioning Adolf Hitler and hissing - imitating the sounds of gas in reference to the gassing of Jews during the Holocaust.
In addition, there was also abuse aimed towards Tottenham fans following the attack on Spurs fans in Rome last week ahead of their Europa League clash with Lazio.
Taunts of "Viva Lazio" and "Can we stab you every week" were heard from the away end in a game which Spurs won 3-1.
While both managers refused to comment on the situation in detail, West Ham boss Sam Allardyce insisted he did not hear any chants, while Andre Villas-Boas said it would not be fair to dwell on the subject for too long.
"I prefer not to mar the performance with a situation like this," Villas-Boas told Sky Sports.
"You know the animosity there is between Tottenham and West Ham and as long as it doesn't reach stupidity it is a great, great rivalry of two London clubs.
"It would be extremely unfair for me to mar the performance of the players but understanding that a couple of situations are avoidable but that we can't decipher the true meaning of what they were saying."
Allardyce said that he would comment on the issue once he knew the facts, but did not want to make a statement before he was sure of what had happened.
"I didn't hear it," Allardyce stated. "I don't hear what the fans say or do when I'm concentrating as a manager on a game of football.
"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?
"I will wait and look at it myself and make a comment once I have listened to what they have said. I don't want to be a political animal, I'm here to talk about football and not what fans are saying and singing."