The 24-year-old finished as top scorer in the Dutch top-flight last season, and he is widely expected to leave Vitesse Arnhem this summer.
Anzhi Makhachkala have already made moves, and one of his agents Francis Kacou has confirmed talks with the Russian giants, a German club and an English side.
Kacou told Algemeen Dagblad: "We have had more than one conversation with Anzhi. We now know what Anzhi would approximately want to pay. About wages, bonuses and commissions we will talk again.
"I have to say we also spoke with a German club last week and the next weekend we will be at a London side. Bony is currently in good demand on the market."
But Sky Sports understands at least three Premier League sides are set to meet with Bony next week.
In recent months, Chelsea, Tottenham, Liverpool and West Ham have all been linked with the Ivorian star.