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.
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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.
Source: Autosport