The New York Post cites sources close to the situation claiming that the Cupertino firm has been unable to agree a per-song rights fee with Sony/ATV.
The iPhone maker is said to be seeking a more flexible rate than music streaming giant Pandora has in place with the major label, but Sony/ATV is reportedly demanding a higher rate from Apple.
Rumours of Apple's internet radio service first emerged last month, when it was reported that the firm is planning to take on Pandora and Spotify in the music streaming sector.
The service is expected to select tunes for users based on their tastes, and provide direct links to iTunes pages where their music can be purchased. It has also been speculated that the platform could be ad-supported, with Apple's iAd supplying marketing.
Apple and the major record labels have declined to comment on the rumoured web radio venture.