Randall Stephenson, CEO of AT&T, speaking at the Business Roundtable CEO Innovation Summit in Washington, DC. on Dec. 6th, 2018. Janhvi Bhojwani | CNBCAT&T and Elliott Management are talking about issues the activist hedge fund raised last month when it pushed for change at the U.S. telecommunications and media conglomerate, two people familiar with the matter said on Thursday.Elliott is pressing the telecommunications giant to cut costs, make management changes and scale back expansion aspirations in one of its most ambitious investor campaigns to date.The two sides have held discussions and there is dialogue, one of the sources said. The meetings have taken place since shortly after Elliott, one of the world’s most powerful activist investors, six weeks ago sent a four-part proposal for changes to AT&T. The fund says the changes could lift the share price by at least 60% by the end of 2021.Traditionally, activist investors and management and directors at their target companies arrange meetings after proposals are made to see where there may be common ground.The Wall Street Journal reported on Thursday that the two sides could reach a settlement as soon as this month but cautioned that talks could fall apart.Elliott’s plan ranges from divesting certain businesses, eliminating $5 billion in costs, reviewing how it allocates capital and urging CEO Randall Stephenson, who has led the company since the financial crisis, to stop making acquisitions.Spokesmen for AT&T and for Elliott declined to comment.Elliott’s $3.2 billion stake in AT&T has morphed into one of the industry’s most ambitious campaigns in years not only because of AT&T’s size — it has a market capitalization of $270 billion — but also for the range of issues that Elliott says should be addressed. For Elliott, which has $38 billion in assets under management, this marks one of its biggest corporate targets.AT&T last week announced plans to delay its earnings release, a move that has sparked speculation that the two sides wanted more time for talks to progress.Earnings are now scheduled to be released on Oct. 28, one day before it plans to unveil its HBO Max streaming service at an event in Burbank, Calif.Elliott took aim at AT&T’s $85 billion acquisition of media company TimeWarner Inc last year and the $49 billion purchase of satellite television provider DirecTV in 2015 in its letter. It also said that the company’s board needs directors with domain expertise and operating skills and that it has “identified several leading candidates” to discuss with the board. It did not ask for a specific number of seats on the board.The letter struck a conciliatory note and Jesse Cohn, Elliott’s portfolio manager called AT&T CEO Stephenson the night before the letter was publicized to alert the company, suggesting that talks would begin quickly.AT&T has said that it was already exploring some of the issues Elliott has raised.