On Thursday, Zidane surprised the football world by announcing that he was stepping down from his position as manager of the La Liga giants after winning a third successive Champions League crown.
Tutumlu told Ekstra Bladet: "Last night nobody knew Zidane's plans. That's why it's all new to everyone.
"Of course, I've been in contact with people in the club, and Michael Laudrup is a candidate for the job."
Laudrup's last high-profile role came in the Premier League with Swansea City, which he left in February 2014.