The Spanish star only joined the Serie A giants last summer for a fee of around £7m, but there is already talk that he could be moved on quickly for a huge profit.
Callejon was one of the Naples side’s top performers last term, with his goals and assists helping Rafa Benitez’s men to Italian cup success and Champions League qualification.
This has alerted Chelsea and City, who are both keen to lure the 27-year-old to England.
Blues chief Jose Mourinho coached Callejon during his spell with Real Madrid, and is known to be a fan of the versatile forward after granting him many opportunities during his tenure despite possessing a wealth of other talented options.
‘The Special One’ is also believed to be looking to add more spark to his side in the final third, which the former Espanyol man could help with.
City are also in the battle as they plan to build on their Premier League victory last season and mount a genuine challenge for European honours.
Although Napoli are far from keen to lose one of their star men, receiving a big fee for Callejon could help them to get funds in place to mount a serious move for top target Erik Lamela – who is rumoured to want a return to Italy following a disastrous year at Tottenham.