A London-based 34-year-old man, who does not want to be named reported a number of comments to police last week.
He said: “It’s unlawful and I have no doubt that this could incite racial hatred. I understand some Tottenham fans refer to themselves as the ‘Yid army’, but it does not make these groups acceptable.
“A lot of Facebook’s groups have crossed the line beyond banter between football fans.”
The Metropolitan Police confirmed that a complaint was made on December 17 and is being investigated.
A Facebook spokeswoman said the remarks would be investigated and removed if they broke the site’s terms of use, which ban the uploading of content deemed “racially or ethnically objectionable”.