Real's new coach Bernd Schuster, a former Germany international himself, has expressed his desire to add a player of Ballack's characteristics.
The Robben saga has become rather protracted, with the player stalling over signing a contract extension at Chelsea while his current deal has two years left to run.
The pacy, left-footed winger joined the Londoners from PSV Eindhoven for $22m in 2004 but has had to become accustomed to life on the bench after initially being in outstanding form for the Blues.
President Ramon Calderon promised Robben to bring him to the Bernabeu when he took office last year.