The 19-year-old Germany international is one of the Bundesliga's hottest properties, having scored 10 times in 30 league appearances last season.
After what was his third season with the senior squad, Draxler has been linked with moves to a number of big European clubs, but Raul believes he should continue his development at Schalke.
Speaking after the German side beat Raul's current club Al Sadd 9-0 in a friendly, the 36-year-old said: "Jule would be well-advised to stay here for one or two more years.
"Then I trust him to make the switch to a big club, be it England or Spain. My preference, of course, is Real Madrid."
Draxler, who produced a stunning assist for the first of Raul's two goals in the match, said it had "been an honour" to play alongside him.
The two were close friends during their time at Schalke, forming a good understanding as the club reached the semi-final of the UEFA Champions League in 2011.
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