Verstappen, 21, won two races past year, with a third victory snatched from his grasp after a collision while leading in Brazil, and ended the season fourth overall.
Verstappen clinched the best championship result of his young F1 career last season, rising to fourth in the championship with a stunning podium run in the second half of the year.
"I don't think he lacks anything to take those guys on and he's probably the driver they fear the most", Horner said, according to BBC Sport. I will be with a teammate who is one of the best and most talented of the moment.
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.
Horner said the years would eventually take their toll on Hamilton and Vettel and saw Verstappen - the main man at the team after Australian Daniel Ricciardo left for Renault - as heir apparent. "We've seen in the past year that depending on the circuit, those penalties can have minimal consequences". "He is more worldly, more experienced", said Horner.
Red Bull's second team will be the first to reveal next week, and the big news is Daniil Kvyat's Lazarus act.
Measles infections in Europe hit decade high in 2018
About 600 people a day were vaccinated during the last week of January, compared to 200 people during the same period a year ago . Paul Harris (R-Vancouver) has introduced a measurethat would remove personal belief exemptions for the MMR vaccine.
He did one day by accompanying the stewards at a Formula E race in Morocco last month. Not that he was particularly impressed by Formula E, but he came way from being with the stewards and said: "'Crikey, these guys have got hard decisions to make in terms of do they impose a penalty or do they not'".
He did concede, however, that while he didn't expect Honda to be able to match Ferrari and Mercedes' power outputs in the first few races of the season, his aim for the year was to finish up - as he did in 2018 - as a multiple race victor. "To continue to improve, this is the best situation that can happen to me", he said.
"Charles is a really exciting talent". "Communication has been very honest and very open about areas of strength and weakness".
Horner was sure the Honda partnership would be very different. "[We have been in] very much a customer supplier relationship where effectively we were paying for a first class ticket and you get an economy seat".
"With Honda, it being a true technical partnership, there is much more collective responsibility from both sides rather than being a customer supplier scenario".
Having entered F1 in late-2017 with the junior team, Gasly's only race experience in F1 comes with the Italian outfit.