Horner signed a new multi-year deal to lead Red Bull in December, and it is understood that he is now committed to the outfit for up to five seasons.
In the past, Horner has been linked with a potential move to Ferrari, or a switch into a senior management role in F1 itself, but instead he says it was 'logical' for him to remain where he is for now.
When asked how tempted he was by alternatives in grand prix racing, Horner said: "I joined Red Bull at the beginning and it was an absolutely logical thing to extend my relationship with the team.
"For me, stability is important and we have had that at the team for some time now. [Red Bull owner] Dietrich Mateschitz gave me the opportunity to move into Formula 1, and it was almost a formality to extend my relationship with Red Bull."
One of Horner's key tasks now that his own future is settled is to shore up a new contract with Sebastian Vettel.
This may well depend on securing a longer term deal for senior technical staff including Adrian Newey.
When asked what the contractual situation with Newey was, Horner said: "The last thing I am going to do is tell you the detail of contracts, but Adrian is on a multi-year agreement. As I say, continuity and stability are important."
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