Screenrant reports he said, "I have been hearing for as long as I can remember that CBS, who has the rights to the series, has just been saying they’re not interested. That’s the word I’ve been told."
Abrams is referring to CBS Television Studios which owns the rights to Star Trek and would be the ones that would produce any Star Trek series. CBS did reply to his comment saying "We love the Star Trek franchise, its fan base and the many possibilities for its future when the time is right." In short, they are saying not right now and no idea when.
Now that the days of fictional syndicated TV shows is essentially, the CBS network has zero interested in sci-fi and CW is home to tweendom, the studio has no real home for a new series. At least without handing it off to their competitors like say the SyFy Network. Which probably couldn't afford the show anymore as its budget have been drastically cut when Comcast bought it along with NBC. In addition, the two Trek movies were profitable but their worldwide (around $400 million) did little to make CBS believe there is a large enough audience to support a new series. If the sequel had made a billion then it would probably be an entirely different conversation.
Ironically the best chance for a new series might be after the Abrams-verse version runs its course after the third movie. I just do not see most of the cast (especially Chris Pine and Zoe Saldana) signing up for a fourth Trek, effectively ending the franchise run again until another reboot or revisit. Whatever the future of Trek brings, we probably will not know it until at least after the third film is released so around 2015 (but probably even longer than that).
There is a bright light for those that are not all that enamored with the Abrams vision of Star Trek. When asked about exploring other franchises after Star Wars he said, "There are a few stories I can’t wait to tell. And there are new things we’re developing in-house that are not existing properties. I feel I have inadvertently worked on a number of shows and movies that existed long before my involvement. I couldn’t feel luckier to have gotten a chance to do that. I would say I look forward most to the stories that are to come, that are not based on pre-existing [properties]." I take that to mean after Star Trek 3, he will happily take a producer credit or something but his part in steering the franchise will be effectively ended as he moves on to other things.