Trabzonspor will receive 25 percent of the transfer fee as a result of a clause in his deal from the Black Sea based club to Galatasaray in 2012.
The Lions would however, save €14.5 million over the next three seasons in terms of contract fees if they were to part ways with Yilmaz.
The board are considering letting go of the Turkish international in their bid to fall in line with Financial Fair Play regulations.
Galatasaray are the 21st richest club according to Deloitte in terms of revenues raised but are facing up to a two year ban from UEFA for falling to meet the FFP guidelines.
Lions boss Mustafa Denizli revealed that he is uncertain over the future of Yılmaz following yesterday’s Turkish Cup victory.
“Burak Yılmaz won’t leave. If we receive a serious offer will be consider it… even that would be difficult,” Denizli said.
West Ham boss Slaven Bilic has however, confirmed that Yılmaz is on his transfer list and that his addition to the squad would be welcomed.
Bilic told Hürriyet reporter İzzet Çapa: “There is a striker problem right now at West Ham and if the board agree to sign a forward Burak Yilmaz is on my transfer list.”