Speculation has suggested that Blues boss Jose Mourinho will turn his attention to the Turkey international in January in an effort to bolster his firepower.
A swap deal involving Demba Ba has been mooted, which would allow Gala to fill their attacking void.
The Turkish giants are ruling nothing out ahead of the winter transfer window, with chairman Unal Aysal revealing that he will not stand in Yilmaz's way if a suitable offer is tabled for the prolific forward.
Speaking at the Leaders in Football conference, which is being staged at Stamford Bridge, Aysal said: "If he wants to go and Chelsea are interested then of course, why not?
"I favour Turkish players going to Europe to play in European leagues."
Asked if the Blues had already made an approach, he added: "No, not yet.
"We had some requests from Lazio at the end of the summer, but the deal didn't go through because the conditions were not satisfied."