The Hammers are looking to bring in a new centre-back and have already seen offers for James Tarkowski knocked back by Burnley.
They switched their attention to Saint-Etienne talent Fofana, who is being chased by Leicester, and slapped in an offer for his services.
However, Saint-Etienne have rejected West Ham’s £33m bid, which was made up of £23m and £10m in add-ons, spread over six instalments.
And West Ham have called off their efforts to land the highly rated 19-year-old.
Saint-Etienne are opposed to letting Fofana leave before the transfer window closes early next month, but are expecting to be tested with further offers.
Fofana is keen to move to the Premier League as he bids to take his career to the next level.
Coach Claude Puel though has stressed the importance of Saint-Etienne keeping hold of Fofana.
