By Josh Ong

Published: 08:40 PM EST (05:40 PM PST)

Google cofounders Larry Page and Sergey Brin considered hiring Apple CEO Steve Jobs as the company's first CEO, according to a new documentary.

After interviewing a dozen unsuitable candidates during Google's early years, Page and Brin went to meet Jobs, a personal "hero" of theirs. The pair then asked investor John Doerr, "Why can't he be our CEO?"

The anecdote comes from an episode on Page and Brin from the Bloomberg documentary series "Bloomberg Game Changers." Earlier this month, the Bloomberg series, which looks at "today's most influential leaders," aired an episode on Jobs.

Page and Brin eventually hired Eric Schmidt as the CEO in 2001. Schmidt later served on Apple's board of directors, until increasing competition between Google and Apple led Schmidt to resign in 2009. Google's entry into both the computer and mobile operating system markets caused a conflict of interest.

"Eric has been an excellent Board member for Apple, investing his valuable time, talent, passion and wisdom to help make Apple successful," Jobs said, in announcing Schmidt's resignation. "Unfortunately, as Google enters more of Apple's core businesses, with Android and now Chrome OS, Eric's effectiveness as an Apple Board member will be significantly diminished, since he will have to recuse himself from even larger portions of our meetings due to potential conflicts of interest. Therefore, we have mutually decided that now is the right time for Eric to resign his position on Apple's Board."

Though Apple and Google maintained a close working relationship for years, tension has developed between the two companies. According to The New York Times, Brin and Page considered Jobs a mentor of theirs and were regular visitors to Apple's Cupertino, Calif., campus, but the relationship allegedly turned sour when Google introduced Android, with Jobs left feeling betrayed. In July, Page accused Jobs of "rewriting history" through his suggestion that Google caused the animosity between the two companies.