Sky Sports says the Hammers are looking at alternative targets after Saint Etienne rejected the club's £33m bid forFofana.
West Ham offered £23m plus £10m in potential add ons for the 19-year-old centre-back, with the deal structured over six annual instalments.
The Premier League side do not want to engage in a bidding war for Fofana so will now divert their focus to other centre-back targets.
The Hammers are looking to add a centre-back to their ranks this summer and have seen three bids turned down by Burnley for James Tarkowski, who is now in talks with Leicester over a possible deal worth more than £30m.
Leicester had also been in talks to sign Fofana, who has been vocal on social media of his desire to move on from Ligue 1.