The Hammers made a bid of more than $35m for the Italian, but the Serie A side value the player at more than 50 million dollars.
Positive discussions are taking place between the clubs over a player who scored 16 goals in 36 appearances last season.
There is still dialogue between the clubs and West Ham is interested in a player from the other club.
The 20-year-old is rumored to be leaving the club this summer.
The Irons are waiting for a response from Lille regarding the possible transfer of Amadou Onana.
West ham have been frustrated in their attempts to sign Jesse Lingard on a free transfer after Nottingham Forest made a substantial offer
West ham made a proposal to sign Lingard and are happy with the offer they have on the table. The Hammers are waiting for him.
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, who joined from Paris Saint-Germain for $8.25m.
West ham is looking to improve their squad ahead of a season that will see them compete in the Europa League
It's easy to see why Gianluca scamacca is in high demand. He scored 16 times in Serie A last season and is capable of many more. He took the route to the top.
Scamacca is both an early and late bloomer. When he was a teenager, he traveled to the Netherlands twice in order to find an opportunity. At the age of 21, he was out on loan at Ascoli.
He could command a fee in excess of £40m if he were to follow in the footsteps of Zlatan Ibrahimovic and become Italy's next top scorer. A man is dancing.
Here, you can read Adam Bate's full feature.
Areas which are often overlooked by the public are the key strengths of Broja. He runs with the ball at his feet when he regains possession in the last third.
The Albanian started only 21 league games last season, but only five players recovered more possession in attacking areas.
He is one of the league's elite players for pressing from the front, as well as being one of the top 10 for fast breaks.
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The 20-year-old was able to create space and carry the ball into dangerous areas despite his limited game time.
The youngster has scored 20 goals in just 48 starts for the club, an impressive strike-rate, given he has also been hooked off 35 times.
Here you can read Adam Smith's full feature.
The transfer window will close at 11pm on September 1st.
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