The Dutchman was the only driver to finish on the podium in the final five races of 2018, overtaking world champion Hamilton on track at some point of the final three rounds, and his team boss reckons Verstappen is more equipped to succeed than ever.
Red Bull are starting their first season with new engine partner Honda after ending an often-fractious relationship with Renault, and Horner said he expects them to move forward from past year, when they won four races but were usually "in the void between Mercedes and Ferrari and the rest".
"I don't think he lacks anything that they have, if we can provide him the tools to do the job".
But Horner expressed his confidence that the Dutchman, who became the sport's youngest victor when he won the 2016 Spanish Grand Prix at the age of 18, would be their heir apparent.
Daniel Ricciardo donned Renault overalls for the first time since deciding to leave Red Bull. We would rather see consistent evolution, and if that means taking a penalty or two along the way, as we saw previous year the impact of those penalties at the right venue can be fairly minimal.
Horner says he has grown in the past year and is "in a better place to deal with the challenges he faces". He is worldlier, more experienced. "Whether you penalise or not.' I think that was actually a useful exercise for him to see the other side of the fence", said Horner.
Mercedes and Red Bull are launching their new 2019 cars on the same day next week, February 13, as the sport's teams give a first glimpse of how they have interpreted the new aerodynamic rules for this year.
Red Bull announced the February 13 date on the team's Twitter feed, without details.
Horner was sure the Honda partnership would be very different. It's also exciting, but that really only comes when I'm in the vehicle.
Horner said Honda had shown good progress over the European winter and morale was high.
Horner said Red Bull aimed to be more consistent across all circuits this year, rather than just those where engine power was less of a factor.