Fuller told Entertainment Weekly that he and X-Men director Bryan Singer have spoken about the project.
"Bryan and I are big fans of Trek and have discussed a take on what we would do, and we would love to do it," he admitted.
JJ Abrams is currently filming a second Star Trek film, following on from the 2009 movie adaptation.
"I don't think anything is going to happen in any official capacity until after the next movie comes out," said Fuller.
"And I'm sure it would be wisely under JJ Abrams's purview of what happens. He's the guardian of Trek right now."
Fuller previously scripted episodes of both Star Trek: Deep Space Nine and Star Trek: Voyager.
The writer/producer is currently developing the series Hannibal - centred around cannibal killer Hannibal Lecter - and Munsters remake Mockingbird Lane for NBC.
Family Guy's Seth MacFarlane has also admitted that bringing Star Trek back to television would be his dream job.
The Star Trek film sequel will be released on May 17, 2013.
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