It comes as he and Meghan Markle have been warned Netflix, which distributes the show, will “decry” the Royal Family. Season four of the show was released on the streaming service last week, and depicts the troubled relationship between Prince Charles and Princess Diana.
The show has caused controversy due to its depiction of the royals, with analysts claiming Prince William is not happy with the portrayal.
Meanwhile, observers have lined up to speculate about what the show means for Harry and Meghan’s high-profile production deal with Netflix.
The Crown is produced by Left Bank Pictures and Sony Pictures Television.
The Sussexes’ streaming service deal was reported earlier this year, several months after they stepped down as senior royals and moved to California.
Royal commentator Angela Levin claims the couple have made a “terrible error” by agreeing to the deal.
Speaking to talkRADIO she said Prince Harry had once told her he was paying attention to the show but was “‘going to insist it stops before it reaches me.’”
Ms Levin claimed the conversation with Harry took place two years ago.
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Ms Levin called the show “unbalanced” and added: “It’s spiteful. It just goes for people’s negative points rather than their positive ones.”
Contrastingly, royal expert Richard Fitzwilliams has said Harry and Meghan’s Netflix deal will likely not be affected by The Crown.
On Twitter, Mr Fitzwilliam accused series four of the show of being “so nasty” – but has also said the show makes use of “dramatic licence”.
He told The Sun: “We must remember that The Crown has been going for a long time.
“Meghan and Harry will claim the show uses dramatic licence, as indeed it does.”
The analyst added the Duke and Duchess of Sussex “might even be sympathetic” with how some members of the Royal Family are presented.
He said he did not think their production deal with Netflix would be “in any way affected”.
Harry and Meghan’s multi-year deal with the streaming service will see them produce a variety of programmes for its platform.
This is thought to include documentaries and children’s shows. The couple has said they aim to make content “that informs but also gives hope”.