The Federal Trade Commission is looking into whether overlap among the directors of Apple (NSDQ: AAPL) and Google is an antitrust violation, according to a report in The New York Times. U.S. antitrust law prohibits directors from serving on the boards of two competing corporations, although there are some exceptions, including if the competing operations make up only a small percentage of the companies’ total sales. Apple and Google offer competing web browsers and phone operating systems. The companies have two directors in common: Google CEO Eric Schmidt and former Genentech CEO Arthur Levinson (pictured, right). As an Apple director, Schmidt has recused himself from iPhone-related discussions since at least early 2008, according to The New Yorker.

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It’s the second recent antitrust inquiry targeting Google (NSDQ: GOOG). Reports surfaced in both the NYT and the WSJ last week that the Justice Department was concerned that Google’s $125 million settlement with book publishers could give it too much control over book licenses. Both inquiries are reportedly in the preliminary stages and the latest one has a potentially far-quicker resolution: Schmidt and Levinson could simply step down from one of the two boards.

Yet as the NYT points out, the FTC under the Obama administration could pose more challenges to Google. Christine Varney, the assistant attorney general for the Justice Department’s antitrust division, has said very publicly that she is concerned about Google’s power, particularly in the online advertising space.