Raul signed for Schalke on a free transfer from Real Madrid in 2010 and went on to make 97 appearances for the club, scoring 40 goals.
He helped fire them to the Champions League semi-finals in his first season with the Bundesliga side, and the quarter-finals of the Europa League the following year.
Raul is currently at the helm of Real Madrid Castilla and, according to the report, would prefer to stay there than take over at the German side.