That's according to the Independent, which reports the LaLiga giants have reached an 'informal agreement' with the defender.
Rudiger is represented by his brother, Sahr Senesie.
Former Borussia Dortmund attacker Senesie apparently met with Madrid in November.
He is understood to have reached an agreement with Florentino Perez and co. But nothing has yet been signed.
Rudiger, 28, will be eligible to sign a pre-contract with a new club in January 1.
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