Some suggested that Dutchman Verstappen vetoed Sainz's move, citing problems together at Toro Rosso some years ago.
"I don't know where that comes from, because Max is one of the drivers I have the best relationship with in the paddock," Sainz told Dutch publication Formule 1.
As for the talk of a 'veto', Sainz added: "He would never do that.
"I can only be grateful to Red Bull for giving me the opportunity to reach Formula 1 and drive for different teams. The fact that I didn't end with a Red Bull seat does not mean that it will never happen."
The 23-year-old also denied that moving from Renault to McLaren is a backwards step in his career.
"I think it's the right place for me at the right time," Sainz insisted.
"The team is being rebuilt and everything is focused on getting back to the front. I have a contract for two years, but the intention is to stay longer and achieve successes together."
The 2018 calendar resumes with the Belgian Grand Prix on Sunday.