The 33-year-old has been strongly linked with a return to Italy in the January transfer window.
“David is staying at Hercules,” Caliendo told Calcionews24.com.
“His relationship with the Spanish side is very good and he is focused on reaching their objective which is survival.
“He has done very well so far in Spain and he can feel the trust. Italian clubs? Trezeguet is a Hercules player.”
Trezeguet joined Hercules from Juventus in the summer.