The 26-year-old signed for Lille in 2017 from Saint-Etienne for a fee of £8m, going on to make 23 appearances for the club.
West Ham have already made five signings so far this transfer window, including winger Felipe Anderson from Lazio for a club-record £36m.
However, the Hammers are looking to strengthen their defensive options as well, as are newly-promoted Fulham.
According to France Football, Napoli and Inter Milan have also joined the race to sign the Frenchman.
West Ham and Fulham have until August 9 to make any additions to their squads ahead of the 2018-19 Premier League season.