"I think his qualities would be a perfect fit at Real Madrid," added the Augsburg-born coach.
"I thought about Michael before he went to Chelsea," added Schuster.
"He was linked with Real back then, when it was clear [Zinedine] Zidane was leaving. He would be the link between midfield and attack and would really be perfect."
There would also be no language barriers in Madrid either, and with the signings of Christoph Metzelder and Christopher Schorch, a third German would find it easier to settle in with Los Merengues.