They will have to bid aggressively though, as Callejon is also being sought after by Liverpool and Arsenal.
Blues boss Jose Mourinho would be keen for his team to upgrade with a goalscorer in the wide areas, as Juan Cuadrado is continuing to struggle.
Chelsea already upgraded their attack last summer with the signing of Diego Costa. This move paid dividends, as Costa scored with 20 goals as the Blues secured the 2014-15 Premier League title.
Callejon has become a legitimate goal threat for Napoli, scoring 11 goals in 31 Serie A appearances last term.
Mourinho is hoping to strike gold with the 28-year-old as he did with Costa, but adjusting to the Premier League is never easy.
The Spanish international has spent his last two seasons in Italy while totaling 26 goals throughout his Napoli stint.
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