Sources speaking to Billboard said the YouTube service will focus on listening to music via mobiles, and have free and paid-for options.
The premium version would let users cache music for offline access and would remove ads, while the free option would be unlimited but feature ads. The service is predicted to launch this year.
Google already offers its own streaming music service, Google Play Music All Access.
YouTube told the magazine it was "always working on new and better ways" for people to access its content, but stressed it has "nothing to announce at this time".
However, the move makes some sense: YouTube is already used by many people as a free streaming music service, and the site's mobile app has gained offline viewing and improved playlists - already making it a free way to listen to music on the go.
On the other hand, as Billboard notes, many artists don't put all their tracks on YouTube - although fans may post them unofficially - so the selection can be limited.
That could be mitigated by convincing artists to include their full albums, or by widening the selection of available tracks, possibly by integrating with Google Play Music All Access.
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