Apple’s recent addition of Dr. Eric Schmidt, chief executive officer of Google, to their board of directors has led to speculation about whether this will lead to closer collaboration between Apple and Google.

According to Newsweek’s Steven Levy, it will. He suggests that Apple is likely to deliver Google video as an option within its upcoming iTV wireless video peripheral.

“Is it possible that when iTV ships next year, you may also be able to choose a menu item called Google Video, and then zip through the best of the thousands of user-submitted videos on the search giant’s service?” asks Levy. “Google’s consumer product chief, Marissa Mayer, tells me that indeed, the two companies are engaged in talks.”

The idea of the two companies together to deliver Google content via iTV makes sense. Earlier in the year, Google demonstrated technology that allowed AdSense-like dynamic video ad insertion into television content.

Since most people would prefer to watch Internet video on their television, a Google-Apple mashup could give Apple content to move its iTV box, and could put Google in the position of competing with local broadcasters and cable companies.