A hearing had been scheduled for Feb. 4 on the attorneys' subpoena for reporter Jana Winter.
In a motion made public Monday, Holmes' lawyers say they haven't had time to prepare and asked to rescheduled the hearing for April.
Winter wrote a story shortly after the July 20 shootings citing unnamed law enforcement sources in describing the contents of a notebook Holmes sent to a psychiatrist.
The defense contends the leak violated a gag order. Fox officials didn't immediately return a phone call Monday.
Holmes is charged with killing 12 people and injuring 70.
He hasn't entered a plea.
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