Apple is beginning a serious move into the mobile payment market. According to Re/Code, the company has been interviewing senior executives with industry experience for two new positions.

Jennifer Bailey, who runs Apple’s online store, is heading the effort:

“Their ambitions are very, very serious,” one of the sources said.

The payment service will leverage the more than 600 million credit cards tied to current iTunes accounts:

Using those payment accounts as a foundation, the company is evaluating ways to make it easier for shoppers to buy physical products in apps and on the Web using their iPhones. The company is also considering how it might best help its customers make purchases in physical retail stores using only their phones and payment information stored in their iTunes accounts.

And while mobile payment pioneer Square is quickly running out of money and looking to sell, Apple isn’t interested in making an acquisition. The report said Apple considered a deal, but ultimately decided against it.

On the other hand, PayPal made it clear it wants to partner with Apple regarding any payment system. Re/code said the two companies have continued to have active talks.

Back in January, Apple CEO Tim Cook said during a financial results conference call that mobile payments was one of the thoughts behind the Touch ID functionality introduced with the iPhone 5s.