googleGoogle isn’t content making the Android software that runs on cell phones and other devices. Now it is apparently working on its own Google-branded Android phone, according to Techcrunch.

The upcoming Android device would be thinner than a Motorola Droid (another recently launched Android phone on Verizon), this phone is called the Google Phone. We don’t know if the rumor is true. Google declined comment.

It’s always an interesting choice when a platform creator chooses to make its own platform device. It’s like Microsoft creating the Xbox 360 or Intel building its own computers. It enables one company to have complete control over both hardware and software, but it also turns off potential third-party allies.

Techcrunch says that Google is building a branded phone that it will sell directly through retailers and that the device will ship in early 2010. The phone may be a web-only phone that uses voice-over-Internet protocol.

As an aside, Google is also holding a press event tomorrow to talk about its new Chrome OS, a browser-based operating system that will compete with Android in the market and be the brains of beefier devices such as netbooks or computers.