An individual close to Mr Bezos told the outlet that "there has been zero talk on this."
CNN is potentially an asset that AT&T plans to sell. Following its $85bn acquisition of TimeWarner in 2016, AT&T was tens of billions of dollars in debt.
Rich Greenfield, a technology analyst at independent research firm LightShed Partners, told Fox Business that the possible sale was not shocking.
âItâs not shocking to see this corporation want less exposure to the news (division) but Iâm a little surprised CNN would be the only asset to be sold given they have a much stronger digital platform than the rest of Turnerâs properties,â Mr Greenfield said.
He has also publicly pondered about Mr Bezos buying the news giant. In a list of top potential buyers of the network, Mr Greenfield included Mr Bezos, as well as CBS News through Viacom and NBC News through Comcast.
He said that selling off CNN would make most sense if it was part of a larger sale of all of AT&T's Turner Broadcasting entities, which includes TNT, TBS, truTV, Cartoon Network and Turner Classic Movies.
Despite lagging behind its main competitors Fox News and MSNBC in ratings, CNN is still a profitable company, making it potentially attractive to interested buyers.
Mr Trump has been both a vocal critic of CNN and its current president, Jeff Zucker, as well as Mr Bezos's Washington Post.
Senator Josh Hawley, a Republican who sits on the Judiciary Committee's Subcommittee on Antitrust, Competition Policy and Consumer Rights group retweeted a reporter breaking the news of the potential purchase, and very plainly expressed his opposition to Mr Bezos purchasing CNN.
"One word to this: No." he tweeted.
Though Democratic presidential candidate Joe Biden is far less antagonistic toward Mr Bezos and media companies in general, it is unclear how well such a bid would do under a Biden administration.