Google Inc Chief Executive Eric Schmidt said he will discuss with Apple Inc how his role on its board might change after Google's move to launch a new operating system.

Because Google's new Chrome OS would compete with Apple's own computer software, Schmidt said on Thursday he would talk to the Mac computer maker about whether he should recuse himself from Apple's board.

I'll talk to the Apple people. At the moment, there's no issue, Schmidt told reporters at a Sun Valley media and technology conference organized by boutique investment bank Allen & Co.

While Google and Apple compete directly or indirectly in a number of areas -- the most obvious being the smartphone market -- Google's announcement this week that it will launch an operating system raised more questions about the relationship between their boards.

The U.S. Federal Trade Commission is currently looking into whether the ties between the boards violate antitrust laws. Schmidt and former Genentech CEO Arthur Levinson are directors of both companies.

Under federal antitrust law, a person is not allowed to sit on the board of two companies if it decreases competition between them.

Schmidt began recusing himself from Apple board meetings where the iPhone was discussed after Google launched its own Android mobile phone operating system.

Google's Chrome OS -- expected to debut in netbooks in the second half of 2010 -- would compete directly with Apple's OS X platform.

Schmidt said Chrome, which is based on open-source technology, worked with Apple's Safari browser.

There's a very large collaboration with respect to Chrome and Safari, he said.

Schmidt also said he was kept well abreast of the circumstances surrounding Apple founder Steve Jobs' medical leave of absence.

In January, Jobs began a nearly six-month leave to seek treatment for unspecified health issues. He received a liver transplant while on leave, and returned to work last week.

Apple and its board have been criticized by some observers for failing to disclose the exact state of Jobs' health.

I was extremely well-informed as a board member with what was going on with Steve, Schmidt said. He declined to comment further on the matter.

(Reporting by Yinka Adegoke, writing by Gabriel Madway; Editing by Dhara Ranasinghe)