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Google Inc. (NASDAQ: GOOG) has filed an application with the Federal Communications Commission (FCC) asking for a two-year license to create an “experimental radio service” at the company’s campus in Mountain View, Calif. The radio license seeks to use a part of the licensed spectrum band controlled by Clearwire Corp. (NASDAQ: CLWR). That is the interesting bit.

Clearwire is currently the subject of a takeover struggle between majority owner Sprint Nextel Corp. (NYSE: S), which is itself selling a 70% stake to Japan’s Softbank, and Dish Network Inc. (NASDAQ: DISH), which is actively seeking a way to enter the terrestrial mobile market. Google could clearly afford to outbid either if it really wants to.

As a report in The Wall Street Journal notes, Google does not control any licensed spectrum, and the only reason to use licensed spectrum and not freely available WiFi spectrum is because there may be a business opportunity at hand. The other interesting thing about the spectrum Google is applying to use is that mobile operators in Japan and developing countries like China and Brazil already use this spectrum band for their own wireless networks. Any devices Google builds that are compatible with this U.S.-licensed spectrum will also work in Japan, China and Brazil.

Shares of Clearwire are down about 0.3% in early trading today, at $3.20 in a 52-week range of $0.83 to $3.40. Shares of Google up about 1.4%, at $752.03 in a 52-week range of $556.52 to $774.38.