The Italian sports paper claims that there are as many as three more clubs from the Premier League interested in the 28-year-old attacker.
Chelsea, Arsenal and Tottenham Hotspur all are keeping tabs on the former Real Madrid star, according to Il Corriere Dello Sport.
However, Callejon himself wants to stay at Napoli, according to the report, as he has been won over by new coach Maurizio Sarri.
Should West Ham United make a move for Jose Callejon?
Callejon is a very good attacker who can play both as a winger and as a forward.
The Spain international is full of tricks and pace, and he will certainly enhance of the quality of the current Hammers’ squad.
Last season, the former Espanyol star scored 11 goals and created 57 chances in 38 Serie A appearances.
Callejon had a pass accuracy of 85% and a shot accuracy of 48%, and won 29 headers, 16 dribbles and 39 tackles.
During the 2013-14 campaign, the Spaniard scored 15 goals and created 48 chances in 37 league games.
Callejon had a pass accuracy of 82% and a shot accuracy of 58%, and won 22 headers, 23 dribbles and 43 tackles.