RealNetworks’ streaming music software Rhapsody-To-Go will be submitted to the Apple App Store for approval this week.  When the application gets approved, Rhapsody customers will be able to access on-demand streaming of over 8 million tracks within the company’s library through 3G and WiFi connections.

The application will work with the Apple iPhone and the Apple iPod Touch.  Currently a Rhapsody membership costs about $14.99 per month, but the application itself will be free. Next RealNetworks will be working on a Google Android version of their application.

Spotify, a Rhapsody competitor submitted an application back in July too.  Currently Spotify is not available for download in the U.S.  The announcement was made on the Rhapsody blog.