Recent rumours have linked the reigning double world champion with a move to Ferrari when his deal at Red Bull expires at the end of the 2014 season.
It has even been suggested Vettel has performance-related clauses in his existing deal which could result in him moving to Maranello before then.
But Horner insists the 24-year-old does not have an option in place with Ferrari.
"I can't see that because all contracts have to be declared with the Contract Recognition Board for a kick off," Horner said.
"I've also spoken to Sebastian about it, and he has made it quite clear he hasn't had any dialogue and hasn't signed anything with Ferrari, but I guess the rumour mill will always continue."
Despite the stories filtering out of Italy and Germany regarding Vettel's future, Horner believes the German will remain at Red Bull "for quite a few years to come".
Horner said: "I wouldn't say it's frustrating because most of our team has been going to Ferrari at some point, be it Adrian Newey, Mark Webber or Sebastian. Even I'm supposed to be going there.
"But Sebastian is very comfortable in the team, and the team is very comfortable with him.
"He's been with Red Bull for over 12 years now, and I think he'll be with us for quite a few years to come, so I have no concern over Sebastian and where he'll be in 2013, 2014, or beyond."
Horner believes the relationship and trust built up with Vettel over such a long period is key to a continued future.
Horner added: "His current contract is already pretty long, we're two and a half years away from that point.
"But at the end of the day a piece of paper only reflects what you have agreed.
"A relationship between driver and team goes much deeper than that.
"For a driver to perform at his best he has to feel comfortable in the environment and believe in the team.
"Conversely, the team has to feel comfortable in the driver and have faith and belief in him. It's a two-way street, and that very much exists with Sebastian.
"Of course, you have the mystique of Ferrari, a great team that has been around forever and has had some great drivers.
"But Sebastian's immediate and mid-term thoughts are very much on where he is.
"Seb is focused on success, he is motivated by winning and being in a winning team.
"He is only 24, and I don't think Ferrari is a must for him. He is very happy with where he is, he's achieved great results with us, and is focused on trying to achieve a lot more."
Horner, meanwhile, has confirmed having no cause to admonish the German for peddling a conspiracy theory aired after the European Grand Prix in Valencia nine days ago.
It was suggested the safety car deployed in the wake of Jean-Eric Vergne's crash with Heikki Kovalainen - which occurred when Vettel had a 20-second lead - was unnecessary.
Vettel claimed the safety car "was to break our neck", with Red Bull advisor Helmut Marko fanning the flames by adding it was sent out "to aid the show".
Within a couple of laps of the safety car's return, Vettel was forced out of the race with an alternator problem, sparking his initial anger.
Horner has confirmed Vettel "was pretty frustrated", but added: "On reflection you cannot disagree that from a safety point of view it was right to bring out the safety car.
"But 10 minutes after the event he came over to the pit wall and was remarkably calm, taking real comfort in the fact the car was really quick.
"To that point it was our most competitive showing in a grand prix this year.
"Whilst very annoying to lose a race like that, we drew some comfort from the fact the car was so quick, and he was keen to reassure us of that.
"So I don't think there's too much to read into what he said."