One day after the team confirmed Verstappen, 20, had signed a new three-year deal to run until 2020, Horner stressed that Red Bull had no intention of giving Ricciardo a supporting role.
He also rejected suggestions that Ricciardo would gain from a switch to join Mercedes or Ferrari in a bid to win the world championship.
The Australian said on Friday that he was in no hurry to decide his future -- his contract runs to the end of 2018 -- but would relish a chance to race with three-time world champion Lewis Hamilton.
"Time will tell," said Horner. "Daniel is very happy within the team. If we can provide a competitive car, then I've got every confidence that he will be here in the future.
"He would have the same issues with those teams (Ferrari and Mercedes) and I think Red Bull fits well his personality. The way that we operate he sees he has very equal treatment and that he's not performing a supporting role.
"The way we operate here is that we give both drivers absolute opportunity. Within the other teams, he would be performing very much a supporting role."
"The clear intent is to ensure that we keep Daniel in the car past the end of 2018.
"That's absolutely our goal -- to retain both drivers. For me, it's the best driver line-up that we've had, I think it's probably the best driver line-up on the grid and we're obviously very keen to retain that."
Ricciardo had fuelled rumours of a possible move earlier on Saturday when he said he had always wanted to race with Hamilton or two-time champion Fernando Alonso.
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