CNET claims to have heard from "sources familiar with the negotiations" that the record label has become the first major to reach an agreement for both recorded music and publishing.
Universal Music is said to have already pledged its support to the so-called iRadio service, while it has been suggested that Sony Music Entertainment is reluctant to get on board due to royalty concerns.
However, more recent reports appear to indicate that Apple is offering its partners the same royalty rate as rival service Pandora, or even higher.
iRadio is expected to be an ad-supported platform for mobile devices that features deep iTunes integration, allowing users to purchase songs instantly.
The service is rumoured to be similar to Pandora, but with numerous additional features, such as the option to rewind songs at any time.
Apple is yet to officially announce a move into the music streaming business, but the discovery of a "radio button" on jailbroken iPads earlier this year supported the rumours.
The Cupertino firm has been tipped to lift the lid on iRadio at the Worldwide Developers Conference later this month.