The Hammers have raided Serie A twice already this summer to sign Juventus defender Angelo Ogbonna and Sampdoria midfielder Pedro Obiang, and could now make a third move for a player from Italian football in Koulibaly.
The 24-year-old, who joined Napoli from Belgian side Genk last summer, played 27 games last season under Rafael Benitez, but his future could now be in doubt.
Napoli, under new boss Maurizio Sarri, have just signed Tottenham defender Vlad Chiriches, which could push Kouliably down the pecking order at the Stadio San Paolo.
As a result, it appears that teams are looking to land Kouliably this summer, with TMW reporting that West Ham joined Premier League rivals Everton in the race to sign the utility man.
The 6ft 5in Frenchman primarily played at centre back for Napoli, but has also played in defensive midfield for previous clubs - an area West Ham are looking to strengthen having seen loan star Alex Song return to Barcelona at the end of last season.
A physically dominant player with impressive speed to complement his exceptional strength, Koulibaly could be a versatile option for West Ham given his ability to play in defence and in midfield.
They aren't the only team pursuing him, but having already snapped up two Serie A stars this summer, Slaven Bilic's men may feel confident that they can land a third in Koulibaly this summer.