Eurosport Turkey reports that Chelsea plan to offer striker Demba Ba in part exchange.
Chelsea boss Jose Mourinho is reportedly a long-term admirer of the 28-year-old striker who is valued at around £20million by Galatasaray.
Yilmaz almost joined Lazio during the last transfer window and has also been strongly linked with the likes of Arsenal and Liverpool.
Demba Ba has fallen down the pecking order at Chelsea and has been linked with the likes of Arsenal, West Ham, Newcastle and Roma in recent months.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.