The "staggeringly talented" actress will play the princess between the ages of 18 and 22.
The producers of The Crown are looking for someone to play Princess Diana in the hit show.
The Sun reports that series creator Peter Morgan is casting for "a mesmerising new young star with extraordinary range".
The ad reads:
"She has to play charming comedy, flirt and social exhibitionist on the world stage, desperate and lonely self-harmer at her lowest ebb and the kind of psychological intensity of Mia Farrow in Rosemary’s Baby."
Bohemian Rhapsody actress Lucy Boynton is tipped to play Lady Di, as well as Florence Pugh (Little Drummer Girl) and Ellie Bamber (Les Misérables).
The Crown is coming to Netflix this July and will star Oscar-winner Olivia Colman as the Queen and Helena Bonham-Carter as Princess Margaret.