Vettel announced last week he would be leaving Ferrari at the end of the 2020 season after talks over a new contract broke down.
It paved the way for Carlos Sainz to be signed as Vettel's replacement, with Daniel Ricciardo taking Sainz's place at McLaren for next year.
The moves have left Vettel facing an uncertain future in F1, making retirement from the sport a possibility.
Vettel won all four of his world titles with Red Bull in 2010-13 before leaving at the end of the 2014 season, but has remained on good terms with the team.
But Red Bull F1 chief Horner said he did not see a scenario where Vettel could return next year, saying that having two drivers expecting to lead the team rarely ended well.
"I think it's enormously unlikely," Horner said on Sky Sports News.
"We have a long-term agreement with Max [Verstappen]. Alex [Albon] is doing a good job. We've got a good dynamic within the team.
"Experience shows that two alpha males, it doesn't tend to pan out well. Sebastian is still a very competitive grand prix driver. I don't think it would be conducive for our team to have two alphas.
"We're happy with the driver line-up we have. I'm sure he's not short of options moving forward, but he's chosen that it hasn't worked out for him at Ferrari."
Vettel appears to be out of options to remain with a front-running F1 team for 2021, with a move to join Mercedes alongside Lewis Hamilton seeming highly unlikely.
Renault has a vacant seat following Ricciardo's switch to McLaren, but the team has previously said it is keen to get one of its young driver academy members on the grid by 2021.
Asked if he thought it was possible Vettel would retire altogether from F1, Horner said: "That ultimately is his choice.
"He's still relatively young, he's in his early 30s. If he chose to stay, he's obviously still very competitive.
"That's entirely down to him, and nobody will know that apart from Sebastian what his choices are.
"He's got strong values, he's got strong integrity, and I'm sure he will have thought long and hard about this.
"Whether he chooses to continue or not, he's achieved a huge amount during his time in F1. Four world championships, he's one of the most successful drivers of all-time."