Twente have taken only six points from their last five games, including a 3-0 defeat to title rivals PSV Eindhoven on Sunday and a disappointing draw with lowly PEC Zwolle, and also finished bottom of Europa League Group L after failing to win any of their six games.
But they remain third in the Eredivisie, level on points with second-placed Vitesse Arnhem and two behind PSV, and Munsterman played down suggestions that the former England manager is under pressure.
He told De Telegraaf: "Steve is our head coach, our manager in football and that does not change. We really cannot dismiss him, that would have no effect.
"You send someone away and bring in another, but that does not really help.
"McClaren's contract has half a year left on it and we intend for him to serve that, as we have always done - except in the case of (Co) Adriaanse, when relations had broken down."
Adriaanse was sacked in January of this year, halfway through a one-year contract, after a reported disagreement over his tactical approach.
But Munsterman added: "There really is no doubt about McClaren. I am very pleased with the coach because we are still level with the team in second."
Meanwhile, the club's midfielder Rasmus Bengtsson has explained his decision to play the second half of the PSV clash without the protective mask he had been wearing to protect his broken nose.
The Sweden international said: "I had a lot of trouble with it. It hindered my vision and concentration.
"The doctor felt I needed the mask but I decided to play the second half without it, I said I was prepared to take responsibility for the risks. If I had been hit by the ball or an arm, the nose may not heal well and I would look like a boxer.
"In the second half I was not worrying about my nose and was fully focused on the game. Unfortunately it was a bad day, the worst match against PSV since I came here.
"I want to hang up the mask, but it does have a role."