Lloyd Webber and ITV announced plans last Wednesday to launch a series searching for the lead for a remake of the 1970 rock opera.
Rice told The Sunday Telegraph: "I've had several meetings with Andrew and said that I don't want this done, but now it appears it's been signed and sealed.
"Andrew wants to rehash things all the time, but I really don't think Superstar needs that tasteless reality television treatment. Those shows are relentlessly downmarket, which is fine if the show is a lightweight bit of fluff.
"I am fully behind an arena show, but I just don't think you need another television series to do that - it opens up a lot of opportunities for spoofs and I think it would be ill-advised to have people voting for who should be Jesus.
"It's just possible that it might be the most sophisticated, tasteful show hosted by the Archbishop of Canterbury, but I doubt it. It sounds tacky and I really don't think Andrew should do it."
Threatening to overrule the programme's winner, the 67-year-old added: "They can't cast the show without my approval. I have the right to veto casting so if Andrew casts it on TV and I didn't like the person, I could say so."
Finally, Rice revealed that he has contacted ITV as he "does not feel comfortable with the concept of the show".