According to Recode, Apple executives recently met with payment industry partners about the new service, which will reportedly build upon the foundation set by Apple Pay. The service will reportedly be exclusive to Apple users.

In addition to a peer-to-peer payments service, Apple is also reportedly in discussions with Visa about creating its own pre-paid debit cards.

"People would be able to use the Apple cards to spend money sent to them through the new service, without having to wait for it to clear to their bank account," Recode said. "Users could then add the debit card, which may only come in a digital form, to their Apple Pay digital wallet to use for tap-and-pay purchases at brick-and-mortar stores. The card number could also be used to make purchases on websites and in apps."

However, banks are reportedly concerned about Apple potentially offering a debit card, saying the Cupertino company may give the debit card preferential treatment in its services.

An announcement could come as early as this year, though a source warned Recode the payments service may not be introduced at all. Apple has flirted with the idea of unveiling its own peer-to-peer payment service before, with a few different patents popping up over the years.