Two months ago, AT&T chief executive Randall Stephenson stopped by Time Warner chief executive Jeff Bewkes’s offices in New York for a lunch of salmon, while musing about the increasing convergence of the media and telecommunications industries.

During their lunch, Stephenson surprised Bewkes by suggesting that AT&T buy Time Warner, according to people familiar with the matter. Bewkes said it wasn't for sale, but at the right price he would consider an offer, the people said, signaling that a deal was possible.