The Elysium director has ruled himself out as a replacement for JJ Abrams - who may not direct a third Trek film because of his commitments to Star Wars: Episode VII - because he is not interested in movie franchises.
He told German website Filmz.de: "I used to be a Star Trek: The Next Generation fan, like, big time. But no, I probably wouldn't do that.
"I don't know if me getting involved with a franchise is the best thing for me. When studios smell franchises, they smell money. And they'll try to do what they can to the franchise to make it make the most money it can make, and a lot of those interesting ideas kind of fall by the side of the road."
The 33-year-old director - who helmed sci-fi flick District 9 - is a fan of Abrams' Star Trek and his recent sequel, Star Trek Into Darkness, but doesn't feel he would be able to make the movie he wants to make due to restrictions imposed by film studios Paramount and Skydance Productions.
He said: "Do I like Star Trek on its own without the politics of making it? Yes, absolutely. But do I think that you could make it in the way that I would want to make it? Probably not, which makes me not want to make it."