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The screenwriters, who previously admitted that they were scouring through novels based on the franchise, are now contemplating gathering ideas from the original series, Sci Fi Wire reports.
Orci said: "The debate is do you do a story where you go through some familiar things from the series, but now their outcome can be a little bit different, or do you just make it totally new?
"So we'll see. The best idea wins, original or old."
Kurtzman added: "We just had our first 10-minute conversation the other day. We don't have anything yet. I wish we had more to tell you. I think we're really, really pleased to find that, for the most part, the die-hard fans felt that they connected to the material the way they wanted to.
"So I think that enabled us to take a similar approach, which is to say you have to find a way to give everyone a little bit of something, because people will meet you in the middle."
The pair are also attached to pen the project Cowboys And Aliens, which they will work on before the sci-fi follow-up.
Star Trek grossed £70.9m worldwide in its opening weekend.
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