The Lions are currently under investigation by Financial Fair Play and have to keep within the set spending structure this season.
The Istanbul giants were made an from Lazio over the summer transfer window according to Galatasaray sporting director Cenk Ergün who also revealed that they will consider offers for the striker if the price is right.
“Yilmaz is a great striker, we received a lot of offers for him,” Ergun told Sky Sport Italia.
“We even got one from Lazio. If a new proposal arrives we can sit down and talk about it. Everything depends on Burak Yilmaz wishes.”
West Ham are also interested in the prolific striker and also had an offer turned down over the summer according to Goal Turkey.
Hammers boss Slaven Bilic has openly stated in the past that he is a fan of the Galatasaray star who he knows well having coached in Turkey for two-seasons before joining West Ham.
“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.
Yılmaz has lifted the league title and the Turkish Cup twice since joining the club. Yılmaz has three-years left on his contract and is paid in the region of £2.5 million per-season.