The 28-year-old has scored three goals for the Hammers since his £16m summer switch from Bayer Leverkusen, but has often been deployed on the left side of a front three by manager Slaven Bilic.
Reports in Spain emerged on Saturday suggesting that Chicharito had instructed his agent to secure a move to either Sevilla or Valencia in the New Year.
In response to those rumours, the 29-year-old wrote on his official Twitter account: "That's a lie! I'm very happy at West Ham!! #COYI."
Hernandez, who scored in Mexico's 3-1 victory over Trinidad and Tobago on Saturday, has over two-and-a-half years remaining on his contract at West Ham, who currently sit 15th in the Premier League table.