That's the report from TechRadar today. The article quotes Shawn Layden, COO of the Sony Entertainment Network, who says "We will be launching our music service on iOS in the next few weeks."
The Sony executive says the service will be healthy competition with Apple. Music Unlimited is Sony's on-demand service that costs US$9.99 a month. Sony says it has a catalog of 10 million songs. Currently, the service works on selected Sony devices and Android phones. Music Unlimited is not ad-supported.
There's no specific date the service will appear. Sony says to expect it within a few weeks. It's likely Sony will offer a free trial when the app appears in the App Store.