Meeting with reporters Thursday before the company's annual shareholder meeting, Schmidt said resigning from the Apple board "hasn't crossed my mind."
"I don't think Google sees Apple as a primary competitor," Schmidt said, according to the Los Angeles Times.
The FTC is looking into whether it's proper for Schmidt and Arthur D. Levinson, former chief executive of Genentech, to be members of both Google's and Apple's boards. Antitrust rules prohibit companies from sharing board members if they compete in markets that contribute more than 2% of their revenue.
While Google draws the vast amount of its revenue from search advertising, the company does compete with Apple in the mobile phone market. Google developed and is heavily promoting its mobile operating system called Android, which competes with Apple's iPhone platform. Android has been released to the open source community.
Schmidt has said he doesn't participate in board discussions on Apple's iPhone, but it remains to be seen whether that will satisfy the FTC.
Google is no stranger to antitrust inquiries. The Justice Department is currently reviewing a $125 million settlement with book authors and publishers who had sued Google for copyright violations in its scanning of library books.
Last year, Google was forced to abandon an advertising deal with Yahoo to avoid an antitrust battle with the Justice Department.
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