The debate regarding Ecclestone's successor has increased in recent weeks in light of the damages lawsuit being heard in the High Court regarding the sale of the sport to private equity firm CVC in 2006.
The verdict in that case could lead to Ecclestone's sacking as chief executive, as recently suggested by CVC co-founder Donald Mackenzie during the hearing.
With another trial pending in Germany, along with a second lawsuit in the United States, Ecclestone's future - and given he is now 83 - is being drawn into sharper focus.
Two leading figures in industry have previously been mentioned in former Marks and Spencer chairman Sir Stuart Rose and Sainsbury's chief executive Justin King.
Ecclestone, it appears, would prefer someone within F1, with close friend Horner deemed by the octogenarian to be "ideal".
"I would be happy to hold his hand," added Ecclestone, speaking to various newspapers.
"We could have a transitional period.
"It needs someone who knows the sport. If someone comes in from outside, a corporate type, I don't think I could work with them. It wouldn't last five minutes.
"People deal with me because they know me. They know I'm straight with them. That's how it is with Christian. I hope we can do it."
When previously questioned on the subject Horner has often made light of the matter, and suggested it is not for him.
Only recently, Horner said: "Looking at the health Bernie is in he is going to outlive all of us!
"I have no interest in the role he performs. My focus is running a team, and to replace Bernie would be impossible with one person.
"I'm very happy with what I do here. I'm focused and committed to this team."
Speaking to Press Association Sport in the paddock in Sao Paulo ahead of this weekend's Brazilian Grand Prix, Horner has now suggested the possibility of reviewing the matter further down the line.
"I went to dinner with him (Ecclestone) last night and he said to me 'You're going to be mentioned in the papers tomorrow'. I asked him why and he told me," said Horner.
"To be honest, I'm very flattered, but it's all speculation. Right now I am committed to my job."
Asked whether it would be something he would consider in a few years if the position became available, Horner replied: "That is a subject for then.
"But as I say, right now, I'm committed to this team."