The newspaper, citing sources familiar with the matter, said Eddy Cue, Apple's iTunes and App Store chief, "has met with industry executives to discuss Apple's interest in handling payments for physical goods and services on its devices."
Apple manages purchases of digital content in its online store iTunes. Consumers can also buy mobile applications using their iTunes account, meaning the company already has hundreds of millions of credit cards on file.
"In another sign of the company's interest, Apple moved Jennifer Bailey, a longtime executive who was running its online stores, into a new role to build a payment business within the technology giant," the newspaper said, citing "three people with knowledge of the move."
Apple could use the fingerprint reader on its latest model, the iPhone 5s, to limit fraud.
The company last year said it had 575 million registered users with its iTunes store and has sold 375 million iPhones over the last five years and 155 million iPads since its launch in 2010.
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