AT&T Inc. is in talks with Elliott Management Corp. to resolve the activist investor’s campaign for change at the phone and media giant, people familiar with the matter said.

The two sides have held a series of wide-ranging discussions since Elliott disclosed a stake in AT&T five weeks ago and publicly urged the company to make changes aimed at igniting its lackluster share performance. AT&T and Elliott could reach an agreement as soon as this month, though the talks could also fall apart, the people said.

The...