"I hear about people wanting to do movies about my life … dude I'm not dead !!!" she wrote as part of a lengthy caption.
The "Hold Me Closer" singer, 40, did not mention Brown, 18, by name, but her post came after Brown appeared on The Drew Barrymore Show, and said she hoped to one day play Spears on screen.
"I want to play a real person and I think for me, Britney. [It] would be Britney Spears. I think her story, first of all, resonates with me," the British actress told Barrymore. "Just growing up in the public eye, watching her videos, watching interviews of her when she was younger. I mean, same thing with you. I see the scramble for words [in her interviews] and I don't know her, but when I look at pictures of her, I feel like I could tell her story in the right way and hers only."
Bryan Bedder/Getty Images for Samsung, Jon Kopaloff/FilmMagic Millie Bobby Brown, Britney Spears
Biopics on living musicians are relatively common; Coal Miner's Daughter, about the life of Loretta Lynn, the Tina Turner biopic What's Love Got to Do with It, Brian Wilson's Love & Mercy and Rocketman, about Elton John, have all been released while the subject is still alive.
Spears and John teamed up in August for "Hold Me Closer," which marked her first new song in six years. The track — which interpolated John's classic "Tiny Dancer" — peaked at No. 6 on the Billboard Hot 100.
Brown, meanwhile, was cast in Stranger Things when she was 12 years old, and has spent her teen years in the spotlight, just as Spears did. She recently added producer to her resumé with the Enola Holmes series, the second of which hit Netflix earlier this month.