Verstappen has been outspoken about the new crop of cars, saying last week that his Red Bull was not much fun to drive and more like "Formula E on steroids".
A Dutch reporter told Mekies at a press conference during pre-season testing in Bahrain that the driver had said he had not wanted to drive the 2026 car on the simulator last year because he disliked the feeling so much.
"Have you any concerns of him losing interest in this kind of Formula 1?," he was asked.
"Short answer is no," Mekies replied. "Zero concern about that.
"And yes, I do recall our conversation last year when he was switching from a car model to another car model. And yes the difference was so big that at some stage I think rightly he decided to focus on the '25 (car).
"The reality is that the challenge of these regulations is massive...but that's also what we love to try to break through these challenges. Try to find solutions that we felt were not on the table. And that's what we will do with Max."
Verstappen, appearing in a separate press conference with other drivers, said he was just being honest.
The 28-year-old, who lost out to McLaren's Lando Norris last year, also doubled down on concerns about the electrical element, now 50-50 with the internal combustion engine, playing too big a part.
"I don't want us to be close to (all-electric) Formula E. I want us to actually stay away from that and be Formula 1," he said. "Don't increase the battery, actually get rid of that and focus on a nice engine and have Formula E as Formula E, because that's what they are about."
The season starts in Australia on March 8.