Pegg is best-known for his starring roles in the U.K. comedies "Hot Fuzz" and "Shaun of the Dead."
The film will chronicle the early days of James T. Kirk and his fellow USS Enterprise crew members during their time at Starfleet Academy, the trade paper said.
"Just My Luck" and "Smokin' Aces" actor Chris Pine has been offered the role of Kirk.
The movie is slated to start shooting next month.
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