Multiple sources have told The Verge that Amazon is looking into a subscription music service, but so far supposedly talks between Amazon and record companies have been nothing more than informal. It sounds like the plans are aiming towards an on-demand structure, similar to Spotify, rather than a streaming radio option like Pandora.
Amazon already has a huge selection of music available in its MP3 store, and it has the cloud music services set up, just like Google and Apple. So, if it really is aiming for a streaming service, it would have a similar pathway to it as the competition.
source: The Verge