The Lions did also state that West Ham made an offer for the Turkish international striker.
The statement read: “West Ham made a €5 million bid for Burak Yilmaz. He has not submitted a transfer request and we turned down the offer.”
The star striker has played a key role in the Lions lifting the league title for three of the last four seasons.
Yilmaz also played a key role in Galatasaray winning the league title for a record 20th time last season and booking a place in the Champions League for the fourth consecutive season.
The experienced striker did however, sign a bumper four-year contract with the Istanbul giants last season and is one of the highest paid players in the current team.
Yilmaz opened his scoring account in the 2-2 draw against Sivasspor on the opening game of the season last week.