Speaking on the opening day of the Brazilian Grand Prix at Interlagos, he said it was flattering to be connected with the role, but he did not foresee himself leaving his team.
Horner said: "It's very flattering what Bernie has said, but he 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.
"My focus is fully on this team and it is for the foreseeable future. I can't see how any one individual can replace Bernie.
Ecclestone, the commercial boss of the sport, revealed earlier that Horner was his choice to succeed him and run the sport.
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Ecclestone, 83, currently facing legal challenges to his grip on the business he has built and guided over four decades, named Horner, 40, as his preferred successor for the first time, according to British newspaper reports.
"If someone comes in from outside, a corporate type, I don't think I could work with them. It wouldn't last five minutes," Ecclestone told reporters at Interlagos.