The Journal, citing people familiar with the matter, said Apple's service would work on the company's hardware, including the iPhone, iPad and Mac computers, as well as potentially on PCs using Microsoft's Windows operating system.
But it would not work on smartphones and tablets that use Google's Android operating system, as the two technology giants are at loggerheads to dominate the lucrative mobile market.
The licensing negotiations are still at an early stage, the newspaper stressed, adding that it could take months for such a service to launch.
Just as with Pandora, ads would be placed between the music on the would-be service, which would use Apple's iAd platform.
The Journal noted that Apple had previously weighed launching a Pandora competitor, but dropped the bid due to licensing costs.
Pandora reported last week that its revenue climbed in the recently-ended quarter but that it still lost money due in large part to royalties paid out for songs.
The Oakland, California-based firm, which creates personalized radio stations for users, reported a net loss of $5.4 million on revenue that rose 51 per cent to $101.3 million compared with the same period last year.
Pandora went public last year at $16 a share, one of several Internet companies to make their debut on Wall Street in 2011.