The Hammers have reportedly held talks with the defender who is valued around £15m to the Greek side Olympiacos.
Heavy investment has been made in Kurt Zouma and the rewards were there for anyone to see last season, with the experienced French defender leading the line during key games.
There is also strong interest in defender Pape Abou Cisse from Championship side Watford, and Brighton Hove and Albion are also said to be vigorously looking at the details that could bring him to England.
Last January, Newcastle United made an attempt to sign him but Olympiacos held firm and resisted the temptation to cash in on him.
Cisse has had spells in France with Saint-Etienne and Ajaccio but moved to Olympiacos in 2017 where has been by far the best performing defender in Greece.
In total, he has played 132 times for the 47-time Greek league champions, scoring 16 goals.
Check out the latest Premier League transfer speculation below...
1. Juve agree Pogba deal
Juventus have an agreement in principle to sign Paul Pogba on a free transfer following his departure from Manchester United. (Sky Sports) | Liverpool FC via Getty Images
2. Forest in Williams talks
Nottingham Forest are in talks with Liverpool over a £15m deal for defender Neco Williams. (Daily Telegraph) | Getty Images
3. Gunners accept Ballard offer
Arsenal have accepted a bid in the region of £2m from Burnley for Daniel Ballard, with the player given the green light to leave. (Football Insider) | AFP via Getty Images
4. Newcastle to be offered Barbosa
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