The report claims that the Black Eagles have reached an agreement with the player and Hull.
The Black Eagles are expected to complete the transfer over the next few days.
Beşiktaş are in the market for a replacement striker after selling Demba Ba to Shanghai Shenhua for €14 million.
The Senegalese international striker scored a career high 27 goals in all competitions for the Istanbul giants last season and was the teams top scorer.
The Black Eagles have also been in talks with Chelsea striker Loic Remy over the past week but Crystal Palace look favourites to clinch a deal for the France international.
N’doye was closely linked with a move to Trabzonspor but joined Lokomotiv Moscow instead before joining Hull City last January. N’Doye scored five times in 15 games for the Tigers last season.