The rocker admits the idea came to him while the trio was hanging out at Queen's rented Bel Air mansion in Los Angeles.
In his new memoirs Rod: The Autobiography, the singer reveals he "adored" Mercury and thought it would be great to team up with him and long-time pal Elton onstage and in the studio.
He writes, "Elton and I spent a long evening there (in the rented mansion) with Freddie Mercury, a sweet and funny man... discussing the possibility of the three of us forming a supergroup.
"The name we had in mind was Nose, Teeth & Hair, a tribute to each of our remarked-upon physical attributes.
"The general idea was that we could appear dressed like the Beverley Sisters. Somehow this project never came to anything."