The 28-year-old, who hails from the Costa Tropical town of Motril in the province of Granada, could be available for a fee of up to €25 million from Napoli, according to Italian outlet Mediaset.
They report that a meeting will be held between Napoli owner Aurelio De Laurentis and the agent of Callejon, over the coming days. The outcome of this meeting could determine the future of the former Real Madrid youth product.
It is believed that the agent of Callejon will be trying to urge De Laurentis to reduce his valuation, so as to facilitate an easier move to the Vicente Calderon.
Along with his twin brother Juanmi, who is also a winger, Jose Callejon worked his way through the youth system at Real Madrid, with both eventually featuring for the B team, Castilla, although neither could break into the first-team squad.
In 2008, the brothers left Real Madrid, with Juanmi heading to Mallorca and Jose to Espanyol, where he enjoyed an impressive three seasons with the Catalan club.
This form earned Jose a return to Real Madrid in 2011, where he made a total of 77 appearances and scored 20 goals, albeit featuring mainly from the bench as an impact player, over the course of two seasons.
Keen to secure more starting opportunities, Jose Callejon moved on to Napoli for €10 million in the summer of 2013 and has since made 111 appearances, whilst also contributing 32 goals. Good form also earned him his first two caps with the Spanish national team in 2014.
In stark contrast, Juanmi Callejon has had to live in the shadow of his twin brother, spending most of his career in the second-tier of Spanish football, before a spell in Greece with Levadiakos. He then made the surprising decision to quit European football entirely, heading to Club Bolivar in the Bolivian capital of La Paz.