And now reports suggest the east London side are prepared to let Hernandez go in the January transfer window - but who are the favourites to sign him?
Chicarito joined the Hammers from Bayer Leverkusen back in the summer and has since gone on to make 20 appearances for the club.
As things stand Hernandez doesn't look likely to improve any time soon as a West Ham player, with Moyes opting to move the rejuvenated Marko Arnautovic into a striking position alongside Carroll or Michail Antonio, meaning even less chance for him to build up any consistency.
As such, with Diafra Sakho very almost sold to Crystal Palace already, the Hammers will also entertain offers for Chicharito during the January window.
But the former Manchester United man has been a big disappointment so far, scoring only four Premier League goals in 17 games.
Hernandez has struggled to hold down a regular first-team place since David Moyes came in to replace Slaven Bilic at the London Stadium, even though he was snapped up for £16million.
Moyes now intends to reconfigure his attack around other players and offload Hernandez, who earns around £130,000-a-week ($9.1 million per year) and is West Ham's highest-paid player.