The Fanning sisters plan to turn the heiress' 2023 memoir into a TV show, which Dakota called "a dream come true" at the 76th annual Emmy Awards on Sept. 15
"It's early days," Fanning told Laverne Cox on E! Live from the Red Carpet ahead of the 2024 Emmy Awards on Sunday, Sept. 15. "We're in development with it. But we have gotten to know Paris and become friends with her and are going to be a part of telling her story."
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Hilton's 2023 memoir details what it feels like living with ADHD and PTSD from the abuse she experienced in boarding school, as well as navigating fame and dating in the spotlight.
"I think if you told as little girls that we would be friends with Paris Hilton and like, go to her house and see her little dogs and become friends with her and also know the real, the real her, we would have died," Fanning, who received her first Emmy nomination for Ripley, said. "So, we're having pinch-me moments all the time. It's really a dream come true."
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The Perfect Couple actress also told Cox, 52, what she would tell her younger self.
"I think just to keep going and to keep loving it as much as you do," Fanning said. "When you start out when you're young, you bring a real sense of play. That's really what acting is is you're using your imagination, you're playing. And so, I think because I started at 6 years old, I've been able to maintain, or I try to maintain that kind of, like, childlike joy. I would advise to keep that going. I think I'm doing a good job."
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The former child star said she felt "so proud" to be part of Ripley, in which she plays the girlfriend of a man (Johnny Flynn) who's being targeted by a grifter Tom Ripley (Andrew Scott) in 1960s Italy.
"It's been such an incredible journey, you know, filming in Italy," she said. "It took quite a bit of time. And I do feel very transformed by it. It was very challenging for many different reasons, but super fulfilling and watching it and being a small part of it, I just am so proud."
Scott, 47, also earned an Emmy nomination for his role, and Ripley earned a total of 13 Emmy nominations this year.
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See PEOPLE's full coverage of the 76th annual Primetime Emmy Awards as they're broadcasting live on ABC from the Peacock Theater in Los Angeles.