Citing unnamed sources, the neswspaper said on Monday that Google, like Amazon, has yet to secure licenses from the major record companies, and would limit users to a "streaming mode" to prevent piracy.
The new service, expected to be announced at an annual developers conference in San Francisco, would initially be launched in a testing phase, only becoming accessible to the public at a later date, the Journal said.
The newspaper also reported that Apple is currently in talks with major record companies to launch a far more ambitious service than either that offered by Amazon or the new service planned by Google.
Amazon unveiled a service in late March that allows users to store their digital music online and play it on a computer or an Android device.
With Cloud Drive and Cloud Player, users can upload digital music, photos, videos and documents to Amazon servers and access the files through Web browsers or phones and tablet computers running Google's Android software.
Music bought from Amazon.com or Apple's iTunes or from a personal collection is held in a digital "music locker" on the Internet and can be accessed from computers running Internet Explorer, Firefox, Safari or Chrome Web browsers.