Aston Villa have also been linked with the World Cup-winning powerhouse, and it will be interesting to see which of the relegation battlers come out tops in the race.
The 31-year-old brings plenty of Premier League experience to the table after making 195 appearances for Blackburn Rovers and Stoke City.
The Hammers could do with Nzonzi in the middle of the park with the duo of Mark Noble and Declan Rice in need of quality cover and competition as the fixtures continue to pile up.
Villa are also missing John McGinn, and Danny Drinkwater could struggle to replicate the influence of the Scotland international.
Nzonzi is currently on a season-long loan with Turkish giants Galatasaray where he has featured in 15 games across all competitions, but an exit could be the cards with West Ham and the Villans looking to bring him back to England.
The Frenchman offers adequate protection and shield to the defence with his power and expertise, and after leaking 34 goals and 44 goals in the top-flight respectively, the Hammers and Dean Smith’s side need such a defensive midfielder in their teams.