In a one-page order, U.S. District Judge Denise Cote on Friday said she will hold a telephone conference on March 13 to consider the government's request for Cook's testimony.
Apple is the sole remaining defendant in the lawsuit brought against the iPhone maker and five other publishers last April for allegedly conspiring to raise prices of e-books to challenge the dominance of Amazon.com Inc.
All of the accused publishers, including Pearson Plc's Penguin Group, News Corp's HarperCollins Publishers Inc and CBS Corp-owned Simon & Schuster Inc, have already settled with Justice Department in the course of the last year.
The order follows a March 6 request by the government for Cook's testimony.
At the Apple trial, to be overseen by Cote in Manhattan, the Justice Department is not seeking monetary damages but a judicial decree that Apple violated antitrust law, court papers show.
Among other things, government lawyers want the judge to issue an order enjoining Apple from engaging in any conduct similar to that alleged in the case.
An Apple spokesman declined to comment.
The case is United States v. Apple Inc et al, U.S. District Court, Southern District of New York, No. 12-02826.
© Thomson Reuters 2013