Arsenal's Jack Wilshere and Marseille's Nicolas N'Koulou (R) in action
The Hammers already have four centre backs, with Angelo Ogbonna, Winston Reid, James Collins and James Tomkins all competing for places under Slaven Bilic.
Yet with question marks over the future of Tomkins, West Ham may be pursuing another centre back, and it appears that N'Koulou has emerged as a top target for the club this summer.
Get French Football News report that West Ham have been in talks with N'Koulou about a possible move to the Olympic Stadium this summer, though they do face some competition from Besiktas and Lyon.
N'Koulou, 26, will be a free agent in just a matter of days, as his Marseille contract expires at the end of June, and clubs are unsurprisingly keen on the idea of landing him on a bargain free transfer.
A Cameroon international with 68 caps for his country, N'Koulou made his name with Monaco before joining Marseille in 2011, and after more than 200 appearances for Marseille, he looks set to leave the club this summer.
A former team-mate of West Ham sensation Dimitri Payet, N'Koulou could be tempted by a reunion at the Olympic Stadium, in what could be another superb move from Bilic and the West Ham hierarchy.
The Hammers have already signed two free agents in midfielder Havard Nordtveit and winger Sofiane Feghouli, and another top free agent signing in N'Koulou would represent another exceptional deal from the Hammers if they can pull it off.
Would you like to see West Ham sign N'Koulou?