According to AS, the two clubs reached a deal over the weekend and personal terms have already been agreed.
The Partenopei are due to pay €10m for the wide attacker, who cost Real Madrid €5.5m from Espanyol in 2011.
Callejon was personally requested by new Napoli Coach Rafa Benitez.
The 26-year-old scored three goals in 30 Liga appearances for Real Madrid last season.
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