Ecclestone had been quoted in the British media as being an 'ideal' figure to replace him when he elects to stand down from his role, with the 40-year-old being a figure who both knows the sport and who could be trusted in the position.
The 83-year-old also said he would prefer not to see the role taken up by someone from outside the sport, with the likes of Justin King and Richard Scudamore having also been mentioned as possible successors.
"Christian would be ideal," he said. “We could have a transitional period. It needs someone who knows the sport.
"People deal with me because they know me. I have known them for a long time and they trust me. They know I am straight with them. That is how it is with Christian. I hope we can do it.
"If someone comes in from the outside, a corporate type, I don't think I could work with them. They wouldn't last five minutes. I don't want anyone who is a corporate type."
Despite Ecclestone's comments however, Horner was quick to downplay his chances of taking on the role.
"It's very flattering but my focus is fully on this team and is for the foreseeable future," he told BBC Sport. "Bernie is going to be here for a long time to come. He's in great shape and is still doing some great deals for the sport.
"I can't see how any one individual can replace Bernie. What he does is unique and it will be a sad day for the sport when he's no longer here."