The Any Dream Will Do winner stepped down from the West End show's lead role at the beginning of the year and was replaced by Gates, who found fame on Pop Idol in 2002.
"I don't think it'd be fair for him to have me in the audience checking out his performance," Mead told Celebs On Sunday magazine.
"I hear he's in great shape, but you need to be when you spend most of the show prancing around in a loincloth."
On his own experience in the role, he added: "I only ever had one wardrobe malfunction, when the loincloth flew off into the orchestra pit. Thank God I had my boxer shorts on underneath."
Mead tied the knot with former Dream judge Denise Van Outen last month.