West Ham have made a bid of more than £34m for Sassuolo striker Gianluca Scamacca, but the Serie A side value the Italian at around £42.6m.
Positive discussions are ongoing between the clubs over the 23-year-old, who scored 16 goals in 36 Serie A appearances last season for Sassuolo.
West Ham also remain interested in Chelsea striker Armando Broja and dialogue between the clubs remains open.
But Blues boss Thomas Tuchel recently played down talk that the 20-year-old is set to leave the club this summer.
The Irons are also awaiting a response from Lille over the potential transfer of midfielder Amadou Onana.
Meanwhile, West Ham have missed out on signing Jesse Lingard on a free transfer after he joined Nottingham Forest on a one-year deal.
West Ham had made a proposal to sign Lingard and were satisfied with the offer they put forward, but the 29-year-old has decided to join the newly-promoted side.
West Ham have made three signings so far this summer with the arrivals of defender Nayef Aguerd, who joined from Rennes for £30m, and goalkeeper Alphonse Areola for £7.75m from Paris Saint-Germain after his successful loan stint last season and midfielder Flynn Downes from Swansea City for an undisclosed fee.
West Ham boss David Moyes is looking to improve his squad ahead of a season that will see West Ham combine Premier League improvement with a first Europa Conference League campaign.
Gianluca Scamacca is in demand and it is easy to see why. He is a 6’5″ Italy international striker who scored 16 times in Serie A last season, a man capable of all sorts of goals. The only surprise is the route that he has taken to the top.
At 23, Scamacca is both early phenomenon and late bloomer. Identified at 15 as one of the brightest talents in Europe, twice he travelled to the Netherlands as a teenager in search of opportunity. But he was still out on loan at Ascoli in Serie B at the age of 21.
Now, after shining for Sassuolo, he is not only seen as the striker around whom Italy should build their attack, but also a man who can command a fee in excess of £40m given that he might just be the heir to Zlatan Ibrahimovic. The big man with the dancing feet.
Broja’s key strengths are in areas which often slip under the radar. He excels at regaining possession in the final third, winning aerials and running with the ball at his feet.
In fact, only five players recovered more possession in attacking areas last term – despite the Albanian starting only 21 league games.
In addition to being among the league’s elite players for pressing from the front, he also ranks among the top 10 for fast breaks.
Despite his limited game time, the 20-year-old clocked 112 touches in the opposition box – achieved by deft movement, creating space and carrying the ball into dangerous areas.
Drilling deeper into his returns over a brief professional career to date, the youngster has produced 20 goals from just 48 starts across all competitions – an impressive strike-rate, given he has also been hooked off 35 times.
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