The Hammers signed Emenike on a six-month loan in January but have a release clause option that will remain on the table until the end of the season.
The Nigerian international striker has two goals in all competitions this season and has made nine appearances for the east London based club this season.
Emenike has revealed that he would like to stay at the club next season after falling out of favour with the fans and board during his last season at Fenerbahce.
Bilic did however, recently deny a clause in Emenike’s contract forcing the club to sign the powerful striker for €11 million if he makes 10 Premier League appearances.
Speaking to Turkish sports newspaper Fanatik Bilic said: “It is absurd we would never have agreed to such a clause and that the club have no obligation to sign him.”
Emenike spent the first half of the season on loan at Al Ain scoring seven times in 11 appearances.