The chairman of the Society of Black Lawyers Peter Herbert confirmed his organisation had already notified police after some Hammers supporters appeared to mock the gassing of Jews in the Holocaust during the match at White Hart Lane.
Asked if he would take the issue to the police, Peter 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."
The Football Association is also set to investigate the apparent abuse.
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 reported abuse came four days after Spurs fan Ashley Mills was stabbed in an attack by Italian hooligans before Tottenham's game in Rome.
West Ham supporters sang "Viva Lazio", "Can we stab you every week?" as well as the hissing sounds alluding to the Holocaust gas chambers.
There were also reportedly chants about Adolf Hitler during the match, which Spurs won 3-1.
The Community Security Trust (CST), a charity that monitors anti-Semitism, said it has received complaints from people in the Jewish community following the Spurs match yesterday, including from people who were at the game.
CST spokesman Mark Gardner said: "The days of English football crowds making massed monkey noises are thankfully gone, but massed anti-Semitic chanting about Hitler and gassing was clearly heard yesterday from a loud section of West Ham fans.
"We have heard such abuse against Spurs before and it risks seriously compromising the work against racism at all levels of the game.
"UEFA and the FA need to take urgent action regarding Lazio and West Ham respectively. Fans who indulge in racist or anti-Semitic behaviour should be arrested, charged and banned.
"We cannot have 'the football family' ignoring, and therefore encouraging, mass Nazi chanting."
West Ham insisted they will take the "strongest possible action" including life bans for any fans found guilty of anti-Semitic chants at Tottenham.
West Ham said in a statement: "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 anti-racism group Kick It Out said it was looking into the reports abuse.
Kick It Out chair Lord Herman Ouseley said: "Kick It Out is following up with both clubs after the reports circulated concerning unacceptable chanting at White Hart Lane and is awaiting reports with further detail."
Tottenham will be submitting video evidence as part of their report to the FA.
A club spokesman said: "We are currently compiling a full report for the Football Association and shall be submitting this with all our evidence including relevant CCTV footage."