The sport's dominant outfit have been shaken by allegations of misconduct against principal Christian Horner by a female employee.
Horner, who denied the allegations, was cleared last week by an independent investigation and the accuser has since been suspended.
Verstappen, whose father Jos has said Horner must go, was asked about Marko's future after qualifying on pole position at the Saudi Arabian Grand Prix, round two of the season.
The website reported that the Austrian, 80, could face disciplinary action and be suspended after the race in Jeddah. There was no immediate comment from the team.
"I have a lot of respect for Helmut and, you know, what we have achieved together goes very far. And also, of course, my loyalty to him is very big," Verstappen said in a press conference.
"I've always expressed this to everyone within the team, everyone high up, that he's an important part in my decision-making for all the time in the future as well within the team," added the Dutchman.
Marko was instrumental in bringing Verstappen to Red Bull and giving him a debut as the sport's youngest-ever driver, aged 17, in 2015.
"So, yeah, it's very important that he stays within the team, including, of course, everyone else, because, you know, it's a whole team effort," continued the champion.
"And it's very important that we keep the key people together, because I feel like if such an important pillar falls away, that's also what I've said to the team, that is not good for my situation as well."
"For me, Helmut has to stay, for sure."
A former racer who has overseen Red Bull's young driver programme, Marko was close to the energy drink company's late Austrian co-founder Dietrich Mateschitz.
"I think it's also very important, of course, that you give the man a lot of respect for what he has done," said Verstappen. "And that comes back also to loyalty, you know, and integrity."
