The former Schalke striker has been consistently linked with the coaching position at S04.
Schalke fired sporting director Marc Wilmots, head coach Karel Geraerts and assistant coach Tim Smolders before Christmas.
The German club then wanted to bring in Raúl as the new head coach, but was turned down. The Spaniard chose to stay with Castilla.
Schalke then decided to bring in Kees van Wonderen as a replacement for Geraerts.
Now BILD says Schalke have not yet given up hope of attracting Raúl.
The 47-year-old's contract with Real Madrid expires in the summer and he is expected to move on in his career.
If Schalke chooses to part ways with Van Wonderen this summer, they will make another attempt for Raúl.
Schalke is in twelfth place in the 2.Bundesliga after 24 rounds.