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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.