Verstappen has a deal that runs to 2028, although as is normal practice in F1, there are believed to be some escape clauses that would allow him to go elsewhere before the contract's official end.
In the wake of the ongoing controversy involving Horner, there is currently considerable tension between the team boss and Verstappen's father Jos, with the latter saying in Bahrain that the team risked being "torn apart".
Verstappen Sr was also spotted talking to Mercedes boss Toto Wolff, stoking speculation that he sees the Brackley team as a potential destination for his son should he leave Red Bull.
PLUS: How F1's mad tea-party driver market could look if Verstappen moves to Mercedes
Asked in Jeddah if he was confident that Verstappen will stay until the end of the contract, Horner remained bullish.
"I'm certain that he will," he said. "He's got a great team around him. He's got great faith in that team. And we've achieved an awful lot together. So he's committed to an agreement until 2028."
Horner refused to be drawn on Jos Verstappen's call for him to leave the team, saying that the pair had spoken after the Bahrain race.
However, at that stage, the comments had not been made public.
"I'm obviously aware of the comments that were made," he said. "There was a discussion subsequent to the race. And I think everybody's focus is very much on the future.
"And, as I say, discussions took place following the race in Bahrain, and we're all looking forward."
On Wednesday, Lewis Hamilton made some interesting observations about the role of parents in an F1 driver's career.
Asked about the involvement of Jos in his son's management, Horner said: "Look, obviously Max's father has played a key role in his career, and getting him to F1. But obviously, Jos is his own man.
"Max is his own man, as well. And we've seen him go from being a teenager when he joined us to now, very much a young man that's achieved what he has.
"So it's not for me to comment on relationships between fathers and drivers. They're all unique between the different individuals."
Horner insisted that having spoken to Verstappen Sr in Bahrain, it was time to move on.
"I think it's in everybody's interest, collectively, that we've agreed to move on, to focus on the future," he said.
"We both have a vested interest in his son to get the best and provide the best cars for him and to get the best out of him.
"And he's started the season in the best possible way. He's an outstanding talent. And hopefully, we can continue to provide him with a very competitive car."
