The 26-year-old former Real trainee returned to the Bernabeu from Espanyol in May 2011 and, after scoring 20 league goals in 78 appearances for the capital club, he looks destined to join new Napoli coach and countryman Rafael Benitez at the Stadio San Paolo.
Reports in Italy suggest Napoli have agreed to pay Real 10 million euros for the former Spain Under-21 international.
A statement published on sscnapoli.it today read: "Jose Maria Callejon is in Napoli. The Spanish forward arrived in the city this afternoon and has already visited the Castelvolturno technical centre.
"Callejon will undergo medical tests tomorrow."
Callejon would become former Liverpool and Chelsea boss Benitez's second summer signing following the arrival of Belgian winger Dries Mertens from PSV Eindhoven.
Benitez has been tasked with reinforcing the Azzurri squad for a serious tilt at the Serie A title after last season's second-placed finish behind Juventus under predecessor Walter Mazzarri.
Retaining the services of in-demand striker Edinson Cavani remains a top priority, with Paris St Germain reportedly leading the race to sign the Uruguay international amid interest from Chelsea and Manchester City. Cavani has a much-publicised 63million euro release clause in his current contract.