Yilmaz has become a transfer target for the Hammers, and there have been suggestions that they could take the front man on loan from Galatasaray.
West Ham are looking to strengthen their front line, following injuries to Diafra Sakho and Andy Carroll.
However, the Hammers are only looking at short term options, and that makes doing a deal for Yilmaz complicated.
Galatasaray only want to let the Turkish international leave on a permanent basis, while Yilmaz does not feel a loan move to Upton Park would be right for him.
It means that a deal for Fenerbahce striker Emmanuel Emenike looks for more likely.
Emenike is said to be keen to move to the Premier League, and West Ham just need to agree a loan fee for the striker to get him on board.