McClaren, who has joined the club on a two-year deal to become the first English coach in the Bundesliga, said Dzeko, who scored 22 league goals last season, should stay even if his sale brought in tens of millions of euros to the club.
"Strikers are very, very important. We know the value of strikers like this - 70, 80 or 100 million," McClaren told reporters at his official presentation.
"I would like to keep Dzeko. He is a world-class striker and crucial for the success (of this club)."
The 24-year-old Bosnia international is the target of several top European clubs, after the 2009 Bundesliga champions finished a disappointing eighth this year.
"(The last campaign) was a disappointment to the club. I came here to lead the club back to the top," said former England manager McClaren, who steered Dutch side Twente Enschede to their maiden Dutch championship this year.
He had said in the past few days it was beyond Wolfsburg's control to keep Dzeko, who can leave for a set fee, reported by German media to be about 40 million euros.
"We are fighting tooth and nail to keep him. If we want to be successful we have to keep our best player, as every team does," he told Sky Sports News.
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