The report states that Galatasaray turned down a €5 million offer from the Hammers however, the Turkish international is reported to be unsettled at the Lions.
Yilmaz was left out of Galatasaray’s starting line-up last weekend and was substituted off the field after 50 minutes in his sides 2-1 defeat at the hands of Osmanlispor.
The Turkish international has been closely linked with a move to West Ham since the arrival of Slaven Bilic as head coach.
Bilic knows Yilmaz well having coached in Turkey for the past two seasons.
The Metro reported that West Ham United had agreed personal terms with the Turkish international.
The report claims that the prolific striker has agreed to a £6.4 million per season deal with the London based side.
The Turkish international striker has scored 58 goals in his last 87 games at club level and still has another four-years left on his contract.