The Sin City actress told Collider that she has started a campaign on Twitter to get a role in the science fiction blockbuster.
"I love [Star Trek director] J.J. Abrams, and I've got a petition on Twitter about maybe I could be in the next movie, like a Klingon or something - I could just make a noise or speak some Klingon... I would be happy, I would be very satisfied," she said.
Dawson revealed that she kept her love of the franchise a secret from Unstoppable co-star Chris Pine, who plays James T. Kirk in the revived series.
"I am a big Trekkie, which finally just got disclosed to Chris. I've been trying to play it really cool and I had been pretty good at hiding it from him," she explained. "He clearly doesn't follow me on Twitter, because I'm pretty obvious about it. I was trying to play it cool with him, but now the cat's out of the bag."