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Apple has also approached Taylor Swift, according to the report, and is trying to lock in a deal that would let the revamped Beats Music stream a track from Florence and the Machine's new album due out in June.
The big challenge for Apple will be convincing users to pay for its service, while other streaming apps like Spotify offer a similar experience for free. Apple plans to do this by getting artists to offer exclusive deals to Apple so that people will be motivated to pay for its service, Bloomberg says.
The service, which is expected to be a revamped version of Beats Music that might have a new name, will cost $9.99 per month and $14.99 per month for families, according to the report.
It would also be at direct competition with Jay Z's new streaming music service Tidal, which also costs $9.99 per month. Artists such as Rihanna and Beyonce have already signed on with Tidal to offer exclusive music.
The report from Bloomberg comes after 9to5Mac's Mark Gurman reported in February that Apple would release the music service sometime after the Apple Watch launches. Apple is also expected to be making a version of the app for Android, too.