The new business model would be similar to Nokia's "comes with music" deal with Universal Music last December.
Negotiations are said to rest on a dispute over the price Apple would be willing to pay for access to the music labels' libraries, according to the Financial Times.
Nokia is said to be offering music industry partners almost $80 (£40) a handset, to be divided according to their share of the market, while Apple has so far only offered about $20 a device.
One executive told the Financial Times that consumers would pay a premium of up to $100 for unlimited access to music for the lifetime of the device or a monthly fee of $7 to $8 for a subscription model.
Apple is thought to make a relatively small amount of money from its iTunes store compared with its hardware sales.
The move could help drive demand for a new generation of Apple's hardware as well as providing a boost to the struggling record industry.
Apple is also said to be considering a subscription model where it has a monthly billing relationship with its customers through the mobile phone operators. The drawback with this is that it would only work with iPhones, while the "comes with music" model would work with iPhones and iPods.
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