The Hammers have made a bid for the Dnipro winger which falls short of his release clause, while Liverpool have dropped their interest in the Ukraine international
West Ham are expected to make an improved £11.9 million offer for Yehven Konoplyanka, Goal understands.
The Hammers tabled an opening bid of £9.5 million on Tuesday which is expected to be rejected by Dnipro, according to a source close to the deal.
Goal understands the east London club will return with a second bid which will trigger the 24-year-old's release clause and currently face no opposition for his signature with Liverpool having dropped their interest in the player after his proposed move fell through in the last moments of the January window.
Konoplyanka shot to prominence for Ukraine with some eye-catching displays at Euro 2012 and impressed in the Europa League this season, starring against Tottenham, who also registered interest in the player earlier this year, over two legs in the last 32 of the competition in February.
The Hammers have strengthened significantly this summer by adding Cheikhou Kouyate, Aaron Cresswell, Diego Poyet and Mauro Zarate to their ranks.
However, with Sam Allardyce tasked with leading the club to a top 10 finish and returning an attractive playing style to Upton Park next season, they have targeted a marquee arrival and begun talks over a move for Konoplyanka.
Dnipro are widely regarded as tough negotiators and are expected to reject West Ham's initial offer, though a source close to the deal understands the Premier League club will return with a further bid in the coming weeks.
Dnipro have also held talks with Spurs over Konoplyanka, according to the Ukrainian club's president, Igor Kolomoyski.