Cue the next wave of “Google’s buying Twitter” rumors, despite CEO Eric Schmidt’s best efforts. This, after statements this week by Google co-founder Larry Page and Schmidt, reported today in the Guardian UK.

Speaking at Google’s Zeitgeist Conference, Page admitted that the company has been “losing out to Twitter” in a race to meet Web user’s demand for real-time info, according to the newspaper. That led to Schmidt hinting that Google might be able to partner with fast-growing microblogging site.

The rise of Twitter has sparked speculation that the cash-rich Google could buy the business.

…

“There is a presumption that somehow you cannot have multiple solutions that co-exist,”[Schmidt] said. “We can talk to them … there is all sorts of stuff we can do. We do not have to buy everybody to work with them, the whole principle of the web is people can talk to each other.”

That, of course, has been one of the more fascinating things to me about Twitter — that the stuff built around the service by third-party developers is often more compelling and useful than Twitter itself. Google clearly sees that it, too, can build upon and around Twitter’s platform, offering its users a search of tweets alongside its traditional search.

Such an arrangement would be good news for Twitter, which has said even this week that it wants to remain free and open to users — as well as advertising free. Perhaps Google can serve its ads next to its Twitter search service. But Twitter sees advertising as obtrusive and, according to its executives this week, not interesting.

So how will  Twitter make money? It’s said this week that it will focus on lightweight add-ons to its service aimed at businesses that want to message, interact or learn from its customers.

Google integrating or partnering with Twitter in some way will expose more users to the service in a new way — perhaps one that shows what Twitter’s true value might be: as a resource for finding real-time, relevant information created and curated by more than 6 million Twitter account holders.

And as more people sign on, Twitter would be better positioned to sell those “add-ons” to business and, maybe, even turn a buck.

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Last month, I made a date to speak to a group of Little Rock media freelancers, Freeliance, on what Twitter is and how it can help them. We’ll talk about all that today, plus touch on Twitter’s possible future. More on today’s meeting here.