The 67-year-old actress made her movie debut as Laurie Strode in 1978's Halloween, but her big break could have come when she was just 12 years old because producer and family friend Ray Stark was keen to have her read for the role of the possessed Regan MacNeil but her mum Janet Lee didn't agree.
Curtis said on The Drew Barrymore Show: "He called my mum and said, 'Hey, I'm producing the movie of the book The Exorcist. Will you let Jamie audition for it?'
"And at the time I was probably 12 and, like, cute and kind of sassy and I had some personality, and I'm sure he saw me at a party and was like, 'Oh, she'd be funny.' And my mother said, 'No.' "
The Freakier Friday actress noted Barrymore- who was just seven years old when she appeared in ET the Extra-Terrestrial - didn't get the same "protection" she had as a child.
She said: "My mum really wanted me to have, thank God, a childhood, which I understand you didn't get. You didn't get that option."
Linda Blair was ultimately cast as Regan, earning an Oscar nomination for the role.
Meanwhile, Curtis previously reflected on how much she loved working with Lindsay Lohan on Freakier Friday, this year's sequel to their 2003 comedy Freaky Friday.
She told Variety: "She has taught me so much. She has her team, where her two people would be standing on either side of a camera holding a big light.
"It's Lindsay lighting - that would have been good branding - they hold lights so that we look better.
"So, I've learned a lot from her already. We had a good time. We love each other."
She added to the publication of the second film: "It's a movie for today. It is a happy, nostalgic, funny, sweet, heartfelt Disney movie right at the end of the summer.
"There haven't been a lot of movies for women, and this is a love letter to every mother, grandma, sister, cousin and daughter."
Curtis has several other projects in the works including a TV version of Patricia Cornwell's book Scarpetta alongside Nicole Kidman, scam movie Sender and spy drama Spychosis.
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