"I love JJ 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 told Collider.
She has kept her love of Star Trek quiet from Chris, who played James T Kirk in 2009's Star Trek.
Rosario said: "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.
"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."
In Unstoppable, Chris plays a train conductor who has a frantic race against time to stop a runaway freight train carrying combustible liquids and poisonous gas before it wipes out the city.
Rosario, who plays a train despatcher in the film, said: "We would all call him Kirk behind his back and he really knew how to take those punches. That was what is so genius about him" .
:: Unstoppable opens in cinemas on November 26.