The Hammers signed the Nigerian international striker on a temporary move with an £8.5 million release clause option.
West Ham will have to sign Emenike for the full amount if he makes 10 Premier League appearances.
Emenike has made six appearances in the league so far and it remains to be seen if Hammers boss Slaven Bilic will give him another four appearances.
The 28-year-old striker has two goals in eight appearances for the east London based club this season.
Emenike is reported to be happy at West Ham but it will ultimately be up to Bilic and the board whether they deem the striker worth making an £8.5 million investment in.
Bilic is no stranger to Emenike having coached sides that have played against the striker in Russia and most recent in Turkey for Besiktas.
The Hammers are currently 5th in the Premier League one point behind 4th placed Manchester City.