The option is "designed to work with RIM's BlackBerry Messenger," the newspaper reported, citing unnamed sources who had discussed the service with RIM executives.
The new service, to be known as BBM Music, could be launched "as soon as next week," and allow subscribers to access around 50 songs at one time for an as-yet unspecified price, the report said.
According to the paper, the company has already signed, or are preparing to sign, agreements with four music power houses= Vivendi Universal Music, Sony Music, Warner and EMI.
The move is aimed at attracting younger consumers to the product, which is facing tough competition from Apple's iPhone and others.
According to a study by ComScore published in July, the iPhone is now more widely used than the BlackBerry in the US market.