At present BBC has indicated they have no plans to remove him.
Footage has recently emerged of the Christian boxer making sexist remarks about fellow nominee Jessica Ennis-Hill.
The self-named Gypsy King said: "she slaps up good as well, " and that "when she's got a dress on she looks quite fit."
In the same video Fury is asked about his attitude to female boxers and replies that he is not sexist and that a woman should work if a man does, however he adds: "What I believe is 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."
The petition was orginally started after he made homophobic comments during an interview with the Daily Mail.
I've got more personality than all the other competitors put together,in this years @BBCSPOTY who can compete with my sporting achievement!!— Gypsy King (@Tyson_Fury) December 4, 2015
The Daily Mail defended its interview with Fury on its website after a number of comments.
The site wrote: "On November 8, we published an interview with Tyson Fury in the Mail On Sunday.
"It was an astonishing piece of journalism by Oliver Holt, our Chief Sports Writer.
"In the article, Fury offered controversial views in which he equated homosexuality and abortion with paedophilia, something many readers found highly offensive.
"Fury said: '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 is paedophilia.'
"Fury responded to the subsequent storm of publicity by denying everything. He said Holt had made up the quotes."
The article provides the recorded video with Fury and concludes: "Holt did not lie, he did not misrepresent Fury, and he did not put words into Fury's mouth. Fury spoke openly and offered his opinions without being provoked, but when he realised how much controversy his views had generated, he blamed Holt, attempting to tarnish our writer's professional reputation."
The change.org petition has been signed by more than 50,000 people and states that: "Young people need sports personalities that they can look up to not people who express outrageous homophobic views, which can cause bullying and self-harm."
The Gypsy King, & the heavyweight champion of the world, will not be silenced I'll always speak my mind, Like it or lump it, in Jesus name.— Gypsy King (@Tyson_Fury) December 3, 2015
Fellow boxer, Anthony Joshua has weighed in on the debate, and told heavyweight rival Tyson Fury he needs to conduct himself better in public after the new world champion caused further controversy: "You've got kids to grandmas listening to you so I think there's a time and a place to say certain things.
"I think he has to think before he speaks. He has to be a bit more calculated in what he says.
"But he shouldn't change who he is.
"He has always said outrageous things.
"But I think you should never change who you are - that's important. People are going to like you or hate you.
"Sports and boxing are won on talent, not on personality. He's become heavyweight champion of the world on talent so we have to give him credit but becoming heavyweight champion brings mad responsibility."
On Thursday a Christian MP challenged the world heavyweight boxer to a "head-to-head" in parliament.
Shadow leader of the House, Chris Bryant, who previously worked as an Anglican priest, is unhappy at what he says is Mr Fury's homophobic attitude.