Horwood told Daybreak that the royal would be ideal because of his experience of "taking his clothes off".
"I would like to have someone royal like Prince Harry," said Horwood.
"He's no stranger to taking his clothes off, that comes in handy for all the Latin dances. I think he'd be great."
Horwood also tried to lure Daybreak host Matt Barbet into taking part on the show, commenting: "You're tall, handsome, you'd look lovely in a tight pink little outfit!"
Strictly Come Dancing returns to BBC One in September.
Sophie Ellis-Bextor, Joe McElderry and Donna Air are among this year's rumoured contestants.
'Strictly Come Dancing' 2013 - Rumoured celebrity contestants in pictures: