The young forward recently been linked with a move to Borussia Monchengladbach or Newcastle United, but the club have maintained that it would take a sizable offer to tempt them to part with the player.
On Saturday, De Jong criticised the president over his handling of the situation, branding the board's negotiating tactics "indecent" after they raised his asking price.
However, Munsterman is resolute that the club have not acted improperly, and that the player has no reason to be upset.
"There's no truth in that story," he told De Telegraaf, referencing De Jong's outburst.
"They were not even there during our meeting with Borussia Monchengladbach, so they wouldn't know. Luuk de Jong has signed a contract with Twente and he must continue to train and play matches. Nothing else."
But McClaren, who is in his second spell in charge of the Tukkers, has had his say on the conduct displayed by the 21-year-old.
"This is incredible," McClaren said. "I never expected this situation. It is totally unnecessary. It is only the beginning of July. We have two months of this."
De Jong moved to Twente from De Graafschap in 2009, and scored 25 Eredivisie goals last season.