Quoting reports from Italian outlet SportMediaset, the report claims Callejon has caught the eye of Chelsea after an impressive debut season in Serie A.
He joined Rafael Benitez, the former-Chelsea manager, in Napoli from Real Madrid last summer long with ex-Bernabeu first-team players Raul Albiol and Gonzalo Higuain.
And he's scored 14 league goals in 31 starts for the Serie A club this season, and they currently sit third in the table with one game remaining.
But Jose Mourinho, who managed Callejon at Real Madrid for three years, reportedly wants to bring him to Stamford Bridge this summer as the Chelsea boss begins a rebuild of his attacking options.
Chelsea's trio of strikers have produced disappointing returns this season, and with Samuel Eto'o out of contract and Demba Ba and Fernando Torres out of favour, Mourinho is expected to strengthen this summer.
The report claims Mourinho is ready to sanction a €32m bid for the Spanish 27-year-old, with a view to alternating him with Willian in the starting lineup.
And in the same report, Le 10 Sport suggests Napoli are ready to replace the Chelsea target with Real Madrid winger Angel Di Maria, who could be available for €20m.