West Ham have made Galatasaray an offer according to his agent Ogan Tarhan.
Speaking to Lig Radyo Tarhan said: “West Ham made an offer but we will not enter talks before the Galatasaray – Sivasspor game. After the game we will consider the move but the rumours regarding a €10 million offer are false we have not spoke about money.”
Hammers boss Bilic is reported to be a fan of Yılmaz from his time managing Istanbul rivals Beşiktaş over the past two seasons.
“Burak Yılmaz is a player who has scored over 60 goals in his last two seasons of course I think he is a very good striker,” Bilic was quoted as saying on Lig Tv.
The Turkish international forward netted eight goals in nine Champions League appearances over the 2012-13 season, playing a crucial role in Galatasaray reaching the quarter-finals that year.
Yilmaz still has four-years left on his contract and is the first-choice striker at Galatasaray who booked a place in the Champions League for the fourth consecutive season.
The 29-year-old striker played an important role in the Lions winning the league title for a record 20th time last season.
Galatasaray take on Sivasspor in their opening game of the 2015-16 Super Lig season on the weekend.
West Ham beat Arsenal in their opening game of the Premier League season 2-0 last week at the Emirates.