Hernandez, who joined the Hammers for Bayer Leverkusen for £16m last summer, has struggled to make a significant impact at the London Stadium so far this season.
The Mexican international suffered an injury while on international duty in November and, since the appointment of David Moyes as manager, the 29-year-old has found the net just once in the Premier League.
"There are a number of clubs interested in his services, he's a player everyone knows and is incredibly professional," Eduardo Hernandez told Fox Sports. "Our primary focus is a club in which [Hernandez] can play the most games possible. That's the most important.
"Javier has asked personally for it. He's commented, stated and demanded that we look for a club that really needs a player with his characteristics because what he wants is to play and play and play."
Hernandez could get his wish, however, after Englishman Andy Carroll was ruled out of action for three months following surgery on his ankle.