The London club is looking to make Ndiaye their fifth acquisition after the arrival Pablo Zabaleta and Joe Hart, Javier Hernandez and Marko Arnautovic also on the verge of joining them this summer.
The latest report suggests that the Hammers want Ndiaye to bolster their central midfield and will fight a number of other English suitors and Turkish giants Galatasaray for the 26-year-old.
Crystal Palace, Everton and Newcastle United are also reported to be chasing the Dakar-born man.
According to Sky Sports, West Ham have approached the Ottomans over a potential deal.
Slaven Bilic is said to have been most impressed by the Senegalese internationals ability to score goals from central midfield and believes he would be an added asset.
Ndiaye has hit the back of the net 17 times over the course of two seasons in the Super Lig.