Thompson left the Times in 2020 after eight years and oversaw the publication's transformation from print to digital during his tenure.
The veteran media executive began his career at the British Broadcasting Corporation, where he worked on such programs as "Nine O'Clock News" and "Panorama," and rose to the level of director general.
He could not be reached for comment. A spokesman for CNN's parent company, Warner Bros Discovery, declined a request for comment.
CNN is looking to fill the leadership void created by the departure of former Chairman and Chief Executive Chris Licht, who departed the media company in June less than a week after the Atlantic magazine published a critical report about him.
Licht, who had most recently served at CBS as executive vice president of special programming and executive producer and showrunner for "The Late Show with Stephen Colbert," assumed his role at CNN in May 2022.
He replaced Jeff Zucker, who was forced to resign after failing to disclose a consensual relationship with a colleague.
Among other criticism, Licht had taken heat for CNN's decision to broadcast a May 10 town hall with former Republican President Donald Trump.
During the broadcast Trump repeated falsehoods about his 2020 election loss, said that if elected again he would pardon many supporters convicted of taking part in the Jan. 6, 2021, attack on the U.S. Capitol, and called CNN moderator Kaitlan Collins a "nasty person."
(Reporting by Jahnavi Nidumolu and Chavi Mehta in Bengaluru; Editing by Maju Samuel and Mark Porter)
