The Fanatik newspaper reported that the Hammers are set to make a €10 million move for the Turkish international.
However, Bilic was quoted by Milliyet as saying: “Burak Yilmaz is not a target for us at the moment.”
West Ham were reported to have offered Yilmaz a bid worth €4 million per-season on a three-year deal according to Futbol Arena.
Bilic is familiar with Yilmaz having managed rival Istanbul side Besiktas for two-seasons before being appointed West Ham boss over the summer.
The experienced striker played an important role in Galatasaray winning the league and cup double last season.
The Lions will participate in the Champions League group stages for the fourth consecutive season.
West Ham are in need of a striker as Andy Carroll and Enner Valencia are both injured and other options are limited.