Andy West publicly criticised the broadcaster’s decision to keep the newly-crowned heavyweight champion of the world on the shortlist for the awards in Belfast later this month.
Fury has been the subject of continuing criticism over controversial remarks about the role of woman in society, same-sex relationships and paedophilia.
West has written to BBC Director General Tony Hall about the matter and wrote online: “My employer is hurting me and other gay people by celebrating someone who considers me no better than a paedophile and who believes homosexual people are helping to bring about the end of the world.
“It’s tempting to see him for the laughable idiot he is but sadly there are many other idiots who will be inspired and encourage by his naive, juvenile bigotry. I am ashamed to work for the BBC when it lacks bravery to admit it is making a mistake.”
It is understood West “reprimanded by a manager, told an investigation would be launched into his conduct and warned he could be suspended”.
In an interview with the Daily Mail, 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 one’s paedophilia.”
Despite the ongoing row, Fury, who has had to relinquish one of the world heavyweight title belts he held, has been unrepentant in his posts on Twitter.