The music/tech rumor mill has been grinding away — not yet replete by the release of cloud-based music services from Google and Apple.

Facebook reportedly has a new music service in the works that allows users to play music from services like Spotify through their Facebook page, as well as see what their friends are listening to. Is it time for Apple to get worried?

Both companies declined to confirm the rumor. In fact, at the eG8 forum in Paris, Facebook CEO Mark Zuckerberg also implied that there’s no such deal, stating: “We don’t have the DNA to be a music company or a movie company.”

Facebook‘s next big business could have Mark Zuckerberg singing — and Apple‘s Steve Jobs biting his nails. According to a report by GigaOm, Facebook plans to partner with music streaming service Spotify, as well as other music services and applications, to launch a new social music platform that will allow users to listen to music directly through Facebook, and check out what music their friends are listening to, in real time.

Here’s how GigaOM outlines a possible music service:

• Music Notifications: here you have notifications that show if your friends have listened to songs recommended by you or on your profile.
• Recommended Songs: You can get a list of songs heard and recommended by your friends. You can also play them back by clicking the play icon.
• Top Songs from friends.
• Top Albums from friends, with cover art.
• Recent listens from your friends.
• In the upper-right corner there will be a “happening now” ticker that shows what is happening in your social and musical universe, including songs that your friends are playing. There is some talk that this “Happening Now ticker” would show-up all throughout your music experience and not just on the music dashboard.

According to Business Insider, the new service could become a “billion dollar” business for Facebook. The social network’s goal, says BI‘s Pascal-Emmanuel Gobry, is to “do for music what it did for games: use its social graph to help Facebook users discover music and help music startups get users.”

Of course, with the massive licensing fees that go along with (legally) streaming music, it’s not yet clear how Facebook will make money off the new service. But if Music Dashboard does come to fruition — and works well to boot — then Facebook has the potential to cut into Apple’s iTunes territory.

News of Music Dashboard follows a variety of reports that indicate a rift between Apple and Facebook. Apple’s recent announcement that Twitter — not Facebook — will receive deep-level integration into iOS 5 sparked murmurs that the two companies were at odds. Then, just last week, rumors surfaced that Facebook has a web-based app market place, accessible through mobile Safari, that could compete with Apple’s App Store.

Still, if these rumors turn out to be fact, this could be just the final push the social network needs to become the new location for band promotion and music discovery.