The music maestro, who wrote the score for the 1996 movie, reveals the late King of Pop reached out to enquire about contributing to the soundtrack but, after initially showing some interest, studio executives vetoed the move.
Menken told SlashFilm, "I get a call out of nowhere from Michael's assistant, when Michael was at the Four Seasons Hotel in New York."
"He had to (deal with) allegations about inappropriate behaviour with underage kids, and the break-up with Lisa Marie Presley."
"He's looking to change the subject. And he obviously loves Disney so much. So I mentioned Hunchback. He said he'd love to come to my studio, watch the movie and talk about it."
"So we got in touch with Disney Animation. They said, 'Meet with him! If he likes it... well, see what he says,' " he recalled.
Jackson - who died in 2009, aged 50 - wanted to record three songs for the project but, when Menken relayed the news to Disney bosses, the conversation turned awkward.
"Michael said, 'I would like to produce the songs and record some of them.' (I was like), 'Wow. OK. What do we now?' " he recalled.
"Michael left. We got in touch with Disney. It was like somebody dropped a hot poker into a fragile bowl with explosives. (They said), 'Uh, we'll get back to you about that.' "
It was subsequently left to Menken's manager to tell the "Thriller" hitmaker that his services wouldn't be required by Disney.
He said, "Finally, predictably, the word came back, 'Disney doesn't want to do this with Michael Jackson.' I go, 'OK, could someone tell him this?' You can hear a pin drop, no response, and nobody did (tell him)."
"It fell to my late manager, Scott Shukat, to tell Michael or Michael's attorney."
"In retrospect, it was the right decision," Menken continued although he felt Jackson would have understood aspects of the main character's story. "Quasimodo is a character... if you look at his relationships with his family and his father, I would think there's a lot of identification there."
The singer, who had previously denied child sexual abuse claims in 1993, was charged with multiple accusations of molestation in 2003, but was cleared of all counts in a 2005 trial.