REUTERS/Shannon Stapleton
The plan is still in its early stages as Amazon is in talks with music executives about licensing a larger selection of music. Amazon is looking to release the service in the fall.
Prime, the $99-a-year (£79) subscription service that gives users access to free shipping and video, currently has a music library of around one million songs.
However, the service would be available outside of Prime, according to the report, and would come with its own subscription price. Apple and Spotify both currently charge $9.99 (£9.99) a month for the streaming service, with the latter offering a free - but ad-supported - option.
According to The Post, Amazon is looking at a similar pricing structure as Spotify and Apple, with a discount if the service is bundled with Echo, the virtual assistant.
Amazon has been looking to expand the media offerings of Prime by adding more video content, especially exclusives. The company paid around $250 million (£175 million) for Jeremy Clarkson's new motoring show, which will air exclusively on Prime, and has been working on numerous Prime-only TV shows.
Spotify currently has around 20 million paid-for subscribers, according to the company, while Apple has around 10 million.
Business Insider has reached out to Amazon for comment.