“Burak is one of the most important strikers at Galatasaray and in Turkish football. He is among the players I have an eye on,” Bilic was quoted as saying.
Fanatik reported that the Hammers are set to make a €10 million move for the Turkish international.
Yilmaz did not start in the 2-2 draw against Sivasspor on Saturday 15 August which led to speculation that the prolific striker could be on his way out.
Lions manager Hamza Hamzaoglu did however, underline that the decision was tactical and had nothing to do with any transfer rumours.
“Burak, Podolski and Sneijder all on together would have caused us a problem defensively,” Hamzaoglu was quoted as saying by NTV Spor.
West Ham have reportedly offered Yilmaz an offer worth €4 million per-season on a three-year deal according to Futbol Arena.
The 29-year-old striker still has four-years left on his contract and is the first-choice striker at Galatasaray who won the league and cup double last season.