Stamford Bridge side pursue versatile forward.
Jose Mourinho is ready to offload both Juan Cuadrado and Mohamed Salah and will look to 28-year-old Spanish international Callejon to boost his attacking options.
The versatile Serie A star can play in a supporting striker role but is more regularly used in a wide role and has proven a big success since moving to Naples.
Callejon was one of three Real Madrid players who left the Bernabeu for Napoli in 2013, along with Gonzalo Higuain and Raul Albiol, and has racked up 32 goals in 102 appearances for the San Paolo side.
Napoli failed to secure a Champions League berth for 2015/16 and that fact, coupled with the departure of boss Rafa Benitez, could lead Callejon to be tempted by a move to Stamford Bridge.