The Fenerbahce striker has been linked with a move in recent weeks.
The Hammers were reportedly eyeing up a move for the Fenerbaçhe striker, with Turkish radio station Radyospor reporting a move could be on the cards this month.
Bilic’s side are in need of reinforcements up front at present, with both Diafra Sakho and Andy Carroll currently on the injury list.
They have already been linked with a number of potential signings this month, but the Croatian manager has confirmed that the rumours about Yilmaz are just that at present.
“He is a good player you know,” London 24 reports him saying after the 2-2 draw with Manchester City.
“At the moment it is only rumours. He is a very important player for Galatasary and we are well covered in those positions.
“We are still expecting all our strikers to come back from injury in a couple of weeks time. Players like Yilmaz are always linked with clubs, not just West Ham.”
While Bilic has claimed any move for the Turkish forward is just speculation at present, there is no denying that he would be a welcome addition.
He has been nothing short of a goal-scoring sensation during his time in Turkey over the last five years, having first managed 55 league goals in 75 games for Trabzonspor, and currently sitting on 64 in 104 for Fenerbaçhe.
A move seems unlikely though, with owner David Sullivan recently saying they were over their wage limit, as reported by the London Evening Standard, and the capture of Sam Byram from Leeds United not likely to have helped that situation.