The news follows suggestions external figures like Justin King, the outgoing Sainsbury's chief, or F1 marketing specialist Zak Brown are in fact the more likely picks.
Horner, the Red Bull team boss, has repeatedly denied he is interested in the job, even after a judge last week damagingly found that Ecclestone had paid a "bribe" to Gerhard Gribkowsky.
If convicted of that very offense by a German criminal court later this year, the F1 board would certainly remove the 83-year-old.
Horner, however, said last week he would "never consider" replacing Ecclestone.
"My function and commitment is to Red Bull, and I certainly hope that Bernie will continue for another 20 years," he told Sportbusiness International.
But even in light of Horner's repeated denials, a source close to the Delta Topco board said this week: "There is no doubt Christian fits the bill.
"We need someone with experience of formula one, someone who can deal with television rights and commercial contracts," the source told The Times newspaper.
"The fact that Bernie would train Christian up, in effect, looks like a solution to many of the directors."