Fury, the new world heavyweight champion, has repeatedly refused to back down on his claims that the world would end once homosexuality, abortion and paedophilia were legalised.
He's also been accused of homophobic tweets and sexist comments.
Almost 80,000 people have signed a petition calling on the BBC to remove Fury from its 12-strong shortlist for the BBC Sports Personality of the Year award.
The SNP has written to the BBC asking that he be taken off the list.
Head of Public Policy at the Evangelical Alliance, Simon McCrossan told Premier's News Hour: "Our door is open and we'd only be too happy to help everyone.
"Maybe, going back to scripture, we could think about the idea of discipleship and mentorship, whether that's something he's open to our not, I don't know.
"Certainly, if Tyson wants to contact the Evangelical Alliance we would be more than happy to engage with him."
Fury had previously said that fellow nominee and world heptathlon champion Jessica Ennis-Hill "looks good in a dress" and added: "I know for a million per cent I've got more personality in the end of my little finger than the whole of the nomination group put together."
Fury attempted to clarify his comments to Jeremy Vine on BBC Radio 2, insisting he did not equate homosexuality to paedophilia, but repeating the controversial views he originally made in a pre-fight interview with Mail on Sunday.
Fury told Vine: "Homosexuality, abortion and paedophilia - those three things need to be accomplished before the world finishes - that's what the Bible tells me.
"That isn't my opinion, I didn't say that, that's what the Bible tells me, and that's all I said. I didn't say I had a problem with homosexuals or abortionists or paedophiles, I didn't say I'm with it or against it, I just stated what I am taught through my scriptures."
He added: "I don't think that homosexuals and paedophiles are alike, of course I can tell the difference, two adults consenting to have sex with each other is nothing like an adult messing with a child, is it.
"Let's not make any mistakes I don't think gay people are like paedophiles, that's not what I said.
"Two adults consenting to love each other is a different matter to an adult messing with a child.
"There are lots of things in this life that are sins and whoever hasn't sinned can throw the first stone at me."
The SNP's culture spokesman at Westminster, John Nicolson MP, has written to the BBC asking that Fury be removed from the shortlist.
He told The National newspaper: "It's time we looked into homophobia in sport because it is one of the last great bastions of homophobia in society."
The BBC Sports Personality of the Year award winner will be announced on December 20.
Listen to Simon McCrossan speaking to Premier's Antony Bushfield:
