Gurman says Apple is working on iOS 8.4, a software update that would be released after the Apple Watch goes on sale.
"Apple is currently considering using iOS 8.4 as the iOS update that includes the upcoming Beats-based streaming music service…" says Gurman.
The Apple Watch will go on sale in April, so if Gurman's report is accurate, Apple's streaming music service could debut sometime later that month.
The service itself would integrate directly into the iPhone's music app, as Gurman previously reported, and it may cost around $7.99 per month, although this hasn't been confirmed. Apple is said to be working on an Android version of the app, too.
Apple is also expected to push out an iOS 8.2 update in March that would enable iPhones to connect to the Apple Watch.