Hammers boss Sam Allardyce signed Nzonzi during his time in charge at Blackburn and is thought to be keen to add the Stoke young player of the year to his current Upton Park squad.
Allardyce is looking to get his transfer business done early. Romania captain Razvan Rat signed this week and a deal is in place for Andy Carroll, and Allardyce may now swoop for Nzonzi especially with speculation suggesting Mohamed Diame may leave the club.
With Tony Pulis leaving Stoke it looks as though the France ace has set his sights on a move away.
However, Stoke chairman Peter Coates has said "We are not unduly worried about the situation as he is our player and has three years remaining on his contract."