The 21-year-old Dutchman won two races last year, with a third victory snatched from his grasp after a collision while leading in Brazil, and ended the season fourth overall.
"Max, if you look at his performance in the second half of the [last] year, was the second highest points scorer to Lewis", Horner was quoted as saying by Reuters.
"I think they've had a strong winter", Horner said.
"I don't think he lacks anything that they have".
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.
Former champions Red Bull, who finished third overall behind champions Mercedes and Ferrari previous year, have switched from Renault power units to Honda for the season starting in Australia on March 17. We would rather see consistent evolution, and if that means taking a penalty or two along the way, as we saw past year the impact of those penalties at the right venue can be fairly minimal.
"He's just much more rounded through experience", the Briton continued. "He's just in a better place to be able to deal with the pressures that are placed on him".
Max Verstappen will be looking forward to the coming season
He did one day by accompanying the stewards at a Formula E race in Morocco last month.
But according to the Dutch driver, his new Red Bull RB15 - the first of the team's cars that will feature Honda horsepower - already feels good on the simulator.
"He came back and went, 'Crikey, these guys have got hard decisions to make".
"If I have the vehicle to win then that's what I would love to do".
Horner was sure the Honda partnership would be very different.
"We are going to try to win as many races as possible".
Ferrari enter the season with a new team boss following the replacement of Maurizio Arrivabene with Mattia Binotto, who moves up from technical director. The last five years - obviously we were with Renault for 12 years - and particularly the last three have been very much a customer and supplier relationship where effectively we've been paying for a first class ticket and you get an economy seat.
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