By Katie Marsal

Published: 11:00 AM EST

Google chief executive Eric Schmidt acknowledged this week that his company's foray into the operating system business may further complicate his role as a member of Apple's board of directors.

Schmidt joined Apple's board back in August of 2006, roughly six months before Apple introduced the first iPhone. At the time, Google was primarily enthralled in a battle with Microsoft for share of the online search and advertising markets, while its relationship with Apple was seen as fairly complementary.

Since then, things have got complicated, with the search giant following Apple's iPhone announcement with word that it too would seek share of the mobile handset market through its open-sourced Android operating system. This led to a dicey situation in which Schmidt was forced to begin recusing himself from Apple board meetings when the iPhone was the topic of discussion.

Earlier this week, Google put itself in further competition with Apple -- as well as Microsoft -- when it announced plans to release its own web-centeric computer operating system next year that will target everything from netbooks to full-fledged PCs.

The matter is expected to step up scrutiny of the relationship between the two tech heavyweights by U.S. regulators, as federal antitrust laws prohibit an individual from residing on the board of two companies if that relationship could lead to decreased competition.

Even before Google announced plans for the new Chrome OS based off its nine-month-old web browser, the Federal Trade Commission began looking into the whether the companies were in violation of the Section 8 provision of The Clayton Antitrust Act of 1914, which forbids "interlocking directorates." In addition to Schmidt, Genentech chief executive Arthur Levinson also sits on the board of both companies.

Although Apple and Google now collaborate and compete, their competing products rarely target the same customers. In the case of both web browsers and mobile software, Google aims its offerings at battling the encroachment of Microsoft into its advertising business, with the Google Chrome browser positioned to replace Internet Explorer and the Android phone platform aimed directly at Microsoft's Windows Mobile efforts.

Still, Schmidt said at the Allen & Co media and technology conference in Sun Valley, Idaho, on Thursday that he plans to sit down with his fellow Apple directors and discuss whether it's necessary that he step down from the electronics maker's board at this time.

"I'll talk to the Apple people. At the moment, there's no change," he said, later adding that he was "extremely well-informed as a board member" with respect to the recent medical woes of Apple chief executive Steve Jobs.

Although its too early to speculate on a potential replacement for Schmidt, there have been rumors that Apple, in an effort to further lock down one of its most vital assets, has been considering offering a seat on its board to chief operating officer Tim Cook.