West Ham will probably have to raise their bid for Yevhen Konoplyanka to 15 million euros to activate his release clause if they want to sign the Ukraine winger.
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The Hammers have bid 12 million euros for the 24-year-old but Dnipro Dnipropetrovsk are expected to refuse, a source told ESPN FC.
Konoplyanka, who has scored eight goals in 36 games for his country, is keen to move to England and would be willing to play for West Ham.
They could face competition from Manchester United, who retain an interest in Konoplyanka, although it is looking less likely they will bid for him.
The winger almost joined Liverpool in the January transfer window, when managing director Ian Ayre travelled to Ukraine in a failed attempt to tie up a deal, and was also a target for Tottenham. However, neither Liverpool nor Spurs are in the running for him this summer, while Arsenal, who also monitored his availability, are also not planning to bid.
At 15 million euros, Konoplyanka would become the second most expensive signing in West Ham's history, behind only Andy Carroll, who cost 15 million pounds last summer.
West Ham have already made three signings this summer, bringing in Senegalese midfielder Cheikhou Kouyate from Anderlecht, left-back Aaron Cresswell from Ipswich and midfielder Diego Poyet from Charlton.