The Japan international has featured just sparingly for the Italian giants so far this season, making four Serie A starts with another three appearances coming off the bench.
Predominantly an attacking midfielder, Honda can play in a range of positions in the final third and his energetic style of play would see him become an asset in the Premier League.
The report in The Sun claims that Tottenham Hotspur and Everton have previously been accredited with an interest in the 29-year-old yet it is West Ham United who now appear the most eager to sign him.
“West Ham plan to rev up their top-four charge in January with a £5million move for AC Milan star Keisuke Honda,” the report states.
Considering the Hammers brilliant start to the season, a finish in the European places certainly can’t be ruled out and their imminent stadium move makes them an extremely attractive proposition.
Whereas players like Dimitri Payet, Angelo Ogbonna and Honda would probably have brushed off West Ham attempts in the past, now is a completely different story as the club begins to really take off.
With his contract running out in 2017, Milan are said to be ready to allow the former CSKA Moscow star to move on and a genuine interest in joining the East London outfit is apparent.
Honda has featured 48 times for the San Siro side in all competitions, scoring nine goals.