On Wednesday, the energy drink squad announced that Verstappen signed a multi-year contract that ties him to the team until the end of the 2023 season.
"I spent the holidays fixing the contract," Marko told Auto Bild. "I was very worried about losing Max to Mercedes in 2021."
It is not known exactly how much Verstappen is earning from his new deal, however Marko commented: "The new contract was not cheap. But I didn't feel like playing poker."
The Austrian added that the new contract guarantees Verstappen a top engine, which Marko believes Red Bull has in Honda, as the partnership enters its second year.
Marko continued that he is set to enter negotiations with Honda soon over an extended deal, following on from the Japanese manufacturer's decision to supply Red Bull and Toro Rosso with engines until 2021.
"There will be talks with Honda soon," he said to Auto Motor und Sport. "I'm just waiting for an appointment to be able to fly to Japan."
"If the others want to be even better, they will have to develop dramatically. Max knows what's going on at Honda, he has already seen the new car and he values continuity in the team. In the end there was a common desire from him and from us."
Bahrain International Circuit - Winter testing