The Attack The Block filmmaker hasn't officially signed up, but Paramount and Skydance are said to be keen on him taking the reins on the project, reported Deadline.
However, according to reports Joe was previously offered the chance to direct the sci-fi film but turned it down.
JJ made the first two Star Trek movies but will not be on board for the third as he will be busy making Star Wars Episode VII.
The films star Chris Pine, Zachary Quinto, Simon Pegg and Zoe Saldana.
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