A person contacted Greater Manchester Police after the heavyweight champion clarified his controversial comments about women and gay people on BBC Radio 2 earlier this week.
Greater Manchester Police said: "We take every allegation of hate crime extremely seriously and we will be attending the victim's address to take a statement."
Once a statement has been taken from the alleged victim, Greater Manchester Police will then make a decision on whether to continue with inquiries or not.
Tyson Fury recently said in an interview that: "There are only three things that need to be accomplished before the devil comes home: one of them is homosexuality being legal in countries, one of them is abortion and the other one's paedophilia.
"Who would have thought in the '50s and '60s that those first two would be legalised?"
He also said: "I'm not sexist. I believe a woman's best place is in the kitchen and on her back. That's my personal belief. Making me a good cup of tea, that's what I believe."
Clarifying his comments on the Jeremy Vine Show, Mr Fury said that he did not equate two consenting adults having sex with paedophiles.
The heavweight champion also said: "Tyson Fury loves his fellow humans. He doesn't hate anybody.
"Let's not try and make me out to be some evil person and I hate gays because I don't hate anybody. I can actually say I don't hate anybody.
"The only thing I have for people is love and that's what the world needs to realise. What a man does in his own home and with his own people is his own problems."
A petition for Tyson Fury to be removed from the BBC Sports Personality of the Year award has reached more than 123,000 signatures.
The BBC has come under fire itself after newsreader Clive Myrie used an expletive to describe Mr Fury during an evening paper review earlier this week.
Mr Fury recently became heavyweight champion of the world after beating Wladimir Klitschko. He took the WBO, WBA and IBF title belts from the 39-year-old.
However he lost the IBF title belt less than two weeks after winning after refusing to fight mandatory opponent Vyacheslav Glazkov, to focus instead on a rematch with Ukrainian Klitschko.
