The Black Eagles signed Ba from Chelsea for €7 million last season and club president Fikret Orman recently revealed that there is no player he would not sell for the right price.
The Istanbul giants would be able to double their investment after one season if the deal goes ahead as planned.
The Times also recently linked West Ham and West Brom with the Senegalese international.
The 29-year-old striker did of course play under current West Ham boss Slaven Bilic last season and scored a career high 27 goals in all competitions.
Ba himself stated that he would like to return to the Premier League and believes he still has one more big move ahead of him.
“The fans in Turkey are very passionate and create a great atmosphere but it is no secret that the standard of football is of a lower quality than in England,” Ba told World Soccer.
“The way I left Chelsea was not ideal but that’s life. I am still young and I believe I have another big move left in my career. The Premier League interests me and I am keeping my options open.”
The powerful striker still has two-years left on his current contract with the Black Eagles.