The Germany international is ready to leave the Hammers in January after a difficult 18 months in London,
TMW says Milan are keen and willing to set up a swap involving Mexico international striker Santi Gimenez.
Fullkrug's agent admitted last week that a move could happen over the New Year.
"Many would probably agree with that, seeing Niclas as a classic penalty area striker," Thorsten Wirth told the TOMorrow Business Podcast.
"Strong in the air, physically strong, can shield the ball – so basically made for the Premier League.
"Looking back, we have to say the transfer didn't work out. There's no point in sugarcoating it."
Asked about a January departure, Wirth also stated: "This always has to happen in cooperation with the club, but I believe it can make sense to change something there.
"Time and again, at a point where you said now he's coming, now he'll show England that it wasn't just a good European Championship and then nothing more will come of it – another injury came along, and that's a shame.
"He had a bit of a negative momentum and also some bad luck."