The initiative, launched in the US this week in partnership with Hewlett-Packard, will take advantage of a shift away from traditional music retailing.
It enables customers to buy full-length albums or a personalised compilation from a library of about 250,000 songs.
Marketing has learned that Hear Music has been earmarked for roll-out in the UK later this year to build on the success of Starbucks' wireless internet connection. Chairman Howard Schultz said the US launch was not a test and added that wi-fi access put it in a good position to offer the music service.
Although the price of the service was unavailable as Marketing went to press, it is believed to be comparable to Apple's iTunes, which offers five songs for $6.99 (£3.85).
A spokeswoman for Starbucks in the UK denied a roll-out was imminent.