The 50-year-old had been subject to an internal investigation from Red Bull’s Austrian parent company over alleged ‘inappropriate behaviour’ towards a female colleague.
It has been reported that Verstappen has a clause in his contract – that runs until 2028 – that allows him to leave Red Bull immediately if Helmut Marko departs the team, but Horner has insisted that the Dutchman will see out his long-term deal.
Speaking at the press conference after practice in Saudi Arabia, he said: "I'm certain that he will [see out his long-term contract]. He's got a great team around him, he's got great faith in that team, and we have achieved an awful lot together.
"He's committed to an agreement to 2028 and from the team side, from Max's side, we're determined to build on the success we've achieved already."