The TV show judge described the British royal as "amazing" following his recent headline-grabbing appearance in Las Vegas.
"I would love to see him on Strictly," he told The Daily Telegraph.
"Maybe, if it were a charity event, we might be able to convince him. He gives it large and he's just amazing."
The 47-year-old also joked that he doesn't think he stands a chance of dating the prince.
"I met Prince Harry at Westminster and I want him to be my new boyfriend, but unfortunately I don't think it is going to happen."
Copyright: Rex Features Paul Grover/Rex FeaturesPrince Harry has reportedly been dumped by his girlfriend Cressida Bonas following the leak of naked photos of himself and a mystery woman.
Craig Revel Horwood recently predicted that new Strictly judge Darcey Bussell could be a "bit of a bitch".