Reports suggest that the Premier League club offered about £4 million for the 25-year-old's services, plus Matt Jarvis, who would move to the City Ground on a season-long loan.
The Hammers believe that the addition of Jarvis, a player the club pursued previously in the past, could prove to be decisive if the Premier League club are prepared to up their valuation of the Forest winger.
|Stats per App||Goals||Total Shots||Assists||Key Passes||Pass Accuracy (%)||Successful Dribbles||Fouls Won||Tackles Won||Apps||Mins Played|
Antonio would provide some much needed quality out wide for the Hammers
His link-up play remains dubious - having completed just 60% of his attempted passes and 1.37 key passes per appearance - but he remains a dangerous threat in front of goal.
For a West Ham side lacking a balance between attack and defence in their opening three Premier League fixtures, the Englishman would offer a direct, forward-thinking threat, capable of operating down the flank.
He averaged 3.43 attempts per match last term, while scoring a goal every three matches, finishing the season with 14 successful strikes to his name. Meanwhile, he completed over two dribbles on average.
A move for Antonio - should Forest accept a more substantial bid - would represent an impressive coup for the Hammers.
It is clear to see why the Championship outfit are holding out for a higher offer from the Hammers for one of the division's most accomplished forward-thinking players, especially amid the restrictions of their current transfer embargo.