The as yet untitled movie, starring Reese Witherspoon, will be directed by Todd Haynes, who previously made a biopic about musician Karen Carpenter.
Nora Ephron’s screenplay has been reworked by Pulitzer Prize-winning playwright Doug Wright.
The writer had also been set to direct the film before she died aged 71.
Reese Witherspoon has had a long-standing interest in portraying Peggy Lee, who died in 2002.
Peggy Lee was best known for her hits including Fever and Is That All There Is?.
In 2005, Reese Witherspoon won an Oscar for playing country musician June Carter Cash in Walk The Line, a film about the life of Johnny Cash.
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