"[Page] has good vision. He's very much a strong intellectual. He's a challenging type," said Gillis, adding that Google is a much different beast than it was when Page first ran it as a startup.

"Remember: It's a bigger ship to turn. It's 200 people versus [24,000 employees today]. It's private company versus a public company. This is a lot different," he said.

And word is that Page would like Google to again be run like a hungry young startup -- with less bureaucracy and more innovation, and with fewer middle managers and more engineers.

That means there's a potential management shake-up in the offing.

Rob Enderle, an analyst at Enderle Group, said he wouldn't be surprised if some middle managers were let go in the coming months -- a move that he thinks would be a big mistake.