Recent reports have suggested that the Italian club are prepared to pay around £8.5m for the 21-year-old Spaniard.
"Jose Callejon is in Napoli," read an official statement from the Serie A side.
"The Spanish forward arrived in the city this afternoon and has already visited the Castelvolturno technical centre. Callejon will undergo medical tests tomorrow."
The youngster scored five goals in 38 appearances for Madrid last season.