Bloomberg reported on Friday.
Stephenson will move to the role of executive chairman and oversee a pair of chief executives who will independently manage the company's telecommunications and media businesses, according to the Bloomberg report.
AT&T spokesman Fletcher Cook said in an emailed statement that no decisions on organizational structure have been finalized and that Stephenson and Time Warner Chief Executive Jeff Bewkes were still working through them.
DirecTV will become part of a unit that includes AT&T's traditional phone businesses, to be run by John Donovan.
While AT&T has created one of the world’s leading wireless and TV services, ideal for delivering live shows to phones, movies to homes and even entertainment and news to connected cars, it’s not clear how well executives steeped in the language of phone networks, bits and bytes will be able to resist having a role in creating content.
According to Bloomberg, AT&T is making the foray into media in part because its wireless and pay TV businesses have stopped growing, leaving the company under pressure to find new revenue. In the first quarter, the wireless service lost a record 191,000 subscribers. And on the pay-TV front, customers continue to flee to alternatives like Netflix and Hulu, with a new streaming service, DirecTV Now, doing little to stem the tide.