One source says that AT&T might have to offer as much as $100 billion to get a deal done.
Time Warner and AT&T executives met recently to discuss a possible merger, Bloombergreported on Thursday.
If the informal talks do not lead to a merger, they could result in various other partnerships,Bloomberg said, citing people familiar with the matter.
Time Warner CEO Jeff Bewkes and the rest of the board already turned down a $75 billion offer from 21st Century Fox. One source told The Hollywood Reporter that AT&T might have to offer as much as $100 billion to get a deal done.
The offer from 21st Century Fox that came two years ago was for $85 a share, while Time Warner stock closed Thursday at $82.99, up nearly 5 percent on the day, leaving it with a market cap of $64.6 billion.
Shares of AT&T lost 2 percent on Thursday, closing at $38.65 and leaving it with a market cap of $237.8 billion.
Time Warner had no comment on the merger discussions and AT&T did not respond to a request for comment.
AT&T, run by CEO Randall Stephenson, purchased DirecTV for $48.5 billion last year and is looking to delve deeper into entertainment, people close to the situation say, and Bewkes could support a sale at the right price.
Time Warner, with assets like HBO, Turner, CNN and Warner Bros., has performed well of late, its shares having risen 28 percent so far this year, though the surge is partly due to the fact that the conglomerate is a perceived takeover target.