The off contract Borussia Dortmund defender has an offer from Bologna, but Real are also in contact.
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La Gazzetta dello Sport says Real are considering a move for Hummels.
Nacho Fernández, 34, has left for Al Qadsiah and coach Carlo Ancelotti could replace him with Hummels.
Hummels is said to be a realistic option for Real Madrid, but Bologna are still hopeful of winning the tie.
Bologna have offered Hummels a contract worth €2m-a-year plus bonuses.