Vettel is in need of a new team-mate after Webber yesterday confirmed he is to quit Formula One at the end of this year, bringing to an end 12 seasons in the sport.
Webber - who has rarely seen eye to eye with Vettel, such has been the fractious nature of their relationship - has signed a multi-year deal with Porsche from next year to compete in their sportscar programme.
It leaves the door open for Red Bull to make a high-profile move for red-hot favourite for the vacancy in Lotus' Kimi Raikkonen or promote either Daniel Ricciardo or Jean-Eric Vergne from Toro Rosso.
Other names are potentially in the frame, but whichever way Red Bull choose to go, Vettel is eager to ensure he has a say in the matter.
"It's not my call," said three-times world champion Vettel ahead of this weekend's British Grand Prix.
"Although surely I have a good enough relationship with the team for us to talk about it, not that I expect anything, but it would be nice because obviously I'm staying.
"In an open relationship you talk about the future in general, like certain updates for the car or a route you would like to take.
"Let's say I expect it (a conversation) more when it's about the car more than driver choice, but it would be nice."
As far as Horner is concerned, he has no qualms with Vettel offering his thoughts as to whom he would like his new partner to be from next year.
"Sebastian will be kept in the loop with regard our choice of driver," said Horner.
"His opinion obviously has value because he is out there racing against some of these guys and he sees things we don't, so yes, he will be kept fully in the loop."
Horner, though, claims there is no need to be make a rash decision, believing Webber has given him and owner Dietrich Mateschitz plenty of time to look around.
"We want a fast driver and we want to field the best two cars that we can next year," added Horner.
"We are in a fortunate position in that there are quite a few drivers who would like to drive a Red Bull car.
"We also have two very talented young drivers we have been developing at Toro Rosso and on whom we have an awful lot of information.
"So we don't need to rush into a decision. We will take our time to make sure we make the right decision."