"Tyson Fury is not a role model," the petition says as it accuses him of being homophobic.
The devout-Christian gave the glory to God last weekend when he was crowned the new heavyweight champion of the world after beating Ukrainian Vladimir Klitschko.
Before the fight he tweeted: "Feeling great, blessed be the Lord Jesus Christ".
But he's a controversial character having previously told the Mail on Sunday there were three things that would happen "before the devil comes home".
He said: "One of them is homosexuality being legal in countries, one of them is abortion and the other is paedophilia. Who would have thought in the 50s and 60s that those first two would be legalised?"
In 2013 he was fined £3,000 by the boxing authorities after suggesting opponents were "gay lovers".
Those statements, and previous quotes deemed to be homophobic, have led to the petition being set up.
Mr Fury does not display "the kind of behaviour that merits inclusion on such a well-respected award programme", the petition claims.
But responding to the petition the boxer stood by his comments: "I don't regret anything I've ever said. I'm a man of honour and a man of my word, and what I've said I stick to through thick and thin.
"Whoever wants to challenge me, let them come and challenge me. Whoever doesn't like me, I don't care anyway.
"If you want to give me the award, give it me, and if you don't - keep it."
He's up against Jessica Ennis-Hill, Andy Murray, Lewis Hamilton, Chris Froome, Mo Farah, Kevin Sinfield, Adam Peaty, Lucy Bronze, Max Whitlock, Greg Rutherford and Lizzie Armitstead.