The Hammers are interested in taking the player to the London Stadium, but do not want to be drawn into a bidding war, with Premier League rivals Leicester City also keen on Fofana.
West Ham have offered £23m plus £10m in add-ons for Fofana and have given Saint-Etienne until Friday to make up their mind on the proposal.
David Moyes’ side would also pay the £23m in instalments, with six instalments making up the total package; it remains to be seen if such an arrangement would work for Saint-Etienne.
Saint-Etienne are firmly against letting Fofana go and have knocked back multiple offers from Leicester for the defender.
The Foxes are desperate to land him and are tipped to try again with a fresh proposal.
West Ham do not want to be put up against Leicester in an auction for Fofana and are trying a one-time offer to get the job done.
Fofana has been lauded for his potential and performances for Saint-Etienne, and losing him would be a blow to the French side.
