In a blog posting on RealNetworks’ Web site, Lacy Kemp writes that the company has submitted a Rhapsody application to Apple for review. But getting an official stamp of approval from Steve Jobs & company may be more difficult than writing the actual app.

While no one is doubting the coding capabilities of RealNetworks’ programmers, the sought-after approval by Apple may rely on more than just technical specs. That’s because Rhapsody, which streams music on demand, also sells downloads, putting it in direct competition with Apple’s iTunes Music Store.

Sure, there are other music applications in Apple’s much-celebrated Apps Store, but most are for Internet radio outlets like Pandora, Last.fm and AOL Radio as well as artist-centric apps, tools for musicians and, of course, games.

According to Kemp’s blog posting, the Rhapsody app functions pretty much like the service’s Web site and allows users to log in and listen to anything they want from more than 8 million tracks in the service’s inventory. Heck, with a Rhapsody app on your iPhone, who needs terrestrial radio? Or, for that matter, iTunes.

“There is nothing quite as satisfying as needing to hear a certain song RIGHT NOW and being able to scratch that itch,” Kemp wrote. “That’s what we aim to do, and now it’ll be easier than ever. I can’t even count the number of times I’ve wanted to hear a song on my iPhone and guiltily plopped down $.99 to iTunes to please my impatient self. When I first used the Rhapsody app it seriously felt like the sun shone a little brighter that day. Music matters that much.”

Kemp also reveals that RealNetworks is also working on an app for Android, the mobile operating system initially developed by Google. Anyone wanna bet you’ll see Rhapsody on an Android-powered mobile phone before you see it on the iPhone?

Anyhow, please click here for the complete RealNetworks blog posting about the Rhapsody iPhone app. That is, after you watch their nifty demonstration video embedded below.

Rhapsody on iPhone from Rhapsody on Vimeo.