McClaren, who has taken up the Wolves post after guiding FC Twente to the Dutch title last term, accepts Dzeko's future is out of Wolfsburg's hands at the moment but the Englishman is keen to see the player stay put.
"At the present moment we're not in control of it," McClaren told Sky Sports News.
"He's got a clause in his contract where he can go for a set fee before Monday. After Monday, if nothing happens, we take a little bit more control over the situation and we can dictate it a little bit more.
"He's a world-class striker and we don't want to lose him.
"We're fighting tooth and nail to keep him.
"If we want to be successful we have to keep our best player, as every team does."