"Morgan's U.K. interview shows, including one where former Prime Minister Gordon Brown broke down in tears, impressed CNN bosses. Morgan's show will be prerecorded in New York so he can work 'round his other TV commitments," one insider told the newspaper.
CNN said in a statement it doesn't comment on speculation.
"Rumors that we are close to signing a deal for a Larry King replacement are untrue," the statement said. "Larry is a beloved member of the team, and he will continue to be part of the CNN family into the future."
King, 76, has been in the spotlight recently due to his marriage problems with his seventh wife, Shawn.