AT&T Inc. is exploring parting with its DirecTV unit, people familiar with the matter said, a sharp reversal from Chief Executive Randall Stephenson’s strategy to make the $49 billion bet on the satellite provider a key piece of the phone giant’s future.

The telecom giant has considered various options, including a spinoff of DirecTV into a separate public company and a combination of DirecTV’s assets with Dish Network Corp., its satellite-TV rival, the people said.

AT&T...