West Ham have given Saint-Etienne until Friday to accept their take-it-or-leave-it offer worth £33m for centre-back Wesley Fofana.
Other clubs are interested in the 19-year-old, but West Ham are believed to have made the highest offer so far - which includes an initial fee of £23m and up to £10m in add-ons.
The Hammers, who are proposing to pay the £23m over six annual instalments, do not want to get into a bidding war for the centre-back.
Leicester have also been in talks to sign Fofana, who has been vocal on social media of his desire to move on from Ligue 1.
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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 also on the Foxes' transfer radar.
Despite signing a new contract in April, Fofana has told Saint-Etienne head coach Claude Puel he wants to leave to play in the Premier League and was left out of the club's matchday squad to play Nantes on Sunday evening.
St Etienne originally wanted £25m for their defender, significantly beyond what Leicester are willing to pay to bring him to the King Power Stadium.
Fofana made 24 appearances for St Etienne in a breakthrough campaign last year, as the team qualified for the Europa League and made the French Cup final.
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