The role comes as West attempts to convince the media his marriage is solid after he and Lily James were spotted kissing on their way back to Britain from a film shoot in Italy.
Ironically, the actor's storyline on "The Crown" will deal with Charles' alleged affair with his second wife, Camilla Parker Bowles, while he was married to Princess Diana.
An insider tells The Sun, "Show bosses looked at several stars for the sought-after role, but he was by far their preferred actor. Now both parties are hammering out a deal."
West's representatives have yet to comment on the casting news.
To add to the irony, Lily James recently split from her longtime boyfriend Matt Smith, who portrayed Charles' father, Prince Philip, in the first two seasons of "The Crown".
West's casting news comes as new photos of him kissing James in Rome emerge, while Lily has pulled out of TV appearances to promote her new Netflix film, "Rebecca", amid the scandal.
West insists there's nothing to the photos and he and his wife staged a bizarre show of unity last week, posing for snaps together outside their home in Wiltshire and passing out a note to the U.K. paparazzi, which read, "Our marriage is strong and we're very much still together."
"The Crown" will return with its new season 4 on Netflix on November 15. Olivia Colman stars as Queen Elizabeth, with Gillian Anderson joining the cast as Prime Minister Margaret Thatcher. The season will depict the wedding of Prince Charles and Lady Diana Spencer, played by Josh O'Connor and Emma Corrin respectively.