Raul played for Schalke, beaten 6-1 by Madrid on Wednesday, after leaving the Santiago Bernabeu in 2010.
He spent two years at Veltins-Arena before moving to Qatari side Al Sadd.
AS has cited a report from German publication Sport Bild that quotes Schalke’s president, Clemens Tonnies, as confirming the open offer to the 36-year-old.
“The issue of Raul is always on our minds,” Tonnies said.
“He has a special aura for us and we are a reference for him - that’s what he always says.
“They has always been a possibility for him to return to join us in a different role. We would search for a position for him to fill.”
Raul said prior to the meeting of Schalke and Madrid that such is his affection for the Bundesliga club, he was torn between who to support.
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