Tottenham Hotspur are also believed to be keen on the player.
The Rossoneri have recently sacked their manager Sinisa Mihajlovic and Cristian Brocchi has taken over until the end of the season at least. He is set to change the club’s formation with Honda slipping out of contention.
Tottenham Hotspur have long been linked with the player and CalcioNews24 report that they are keen again.
But it is the interest of West Ham that would seem more likely. The Hammers are looking to advance both on and off the pitch from next season. Honda is not only an excellent player but also brings a fantastic amount of commercial opportunities in his Japanese homeland.
Honda, who joined Milan from CSKA Moscow in 2013, is still one of the most marketable men in his homeland and West Ham would be bringing in a great player for the club.
The 29-year-old, who will be known to West Ham boss Slaven Bilic from his time in Russian football, has played 32 times this season but has managed just two goals in a below par campaign.