The royal was taken on an open-top bus tour of Los Angeles, during which Corden quizzed him about his thoughts on the Netflix drama, including who should portray him as an adult in future episodes.
At first forgetting the actor’s name, Harry suggested fellow redhead Damian Lewis, with Corden saying that the Homeland star was a “great shout”.
“I think Damian Lewis as you and me as William, that’s casting,” Corden said, with Harry sarcastically replying: “It’s not great casting, but it is casting.”
While The Crown will air for two more seasons, with Imelda Staunton taking over the role of Queen Elizabeth from Olivia Colman, Harry and his wife, Meghan, will not be portrayed on the show.
“We have always presented The Crown as a drama, and we have every confidence our members understand it’s a work of fiction that’s broadly based on historical events,” a statement from the streaming service said.
“As a result, we have no plans – and see no need – to add a disclaimer.”
The couple said their new endeavour would be focused on “creating content that informs but also gives hope”.
In the sketch, Corden suggests that Harry and his wife Meghan Markle should find a base in Los Angeles, showing him to the mansion originally used in 1990s sitcom The Fresh Prince of Bel Air.
“If it’s good enough for the Fresh Prince, it’s good enough for a real prince,” Corden said.
Harry and Markle moved to Los Angeles last spring, after revealing that they were stepping back from their role as senior members of the royal family.
“It was stepping back rather than stepping down,” he told Corden. “It was a really difficult environment, which I think a lot of people saw, so I did what any father or husband would do and thought, ‘How do I get my family out of here?’ But we never walked away, and as far as I’m concerned, whatever decisions are made on that side, I will never walk away.”
The appearance marked Harry’s first interview since his grandmother, Queen Elizabeth II, stripped the prince and his wife, the former actress Meghan Markle of their remaining royal duties earlier this month.
The interview is something of a coup for Corden, as it was released ahead of Harry and Meghan’s widely anticipated sit-down with Oprah Winfrey. The Oprah interview is scheduled to air on 7 March.