The 36-year-old midfielder's agent confirmed his client is talking to the Premier League club over a potential switch following his release from the San Siro outfit after 18 years
The 36-year-old's contract at the San Siro expires at the end of June and CEO Adriano Galliani confirmed on Tuesday the club captain would not be retained for the forthcoming season.
Ambrosini spent 18 years with the Rossoneri after arriving from Cesena in 1995 and is now available on a free transfer with Hammers boss Sam Allardyce earmarking the Italy international as a potential transfer target.
Ambrosini's representative, Moreno Roggi, revealed interest from Major League Soccer has been rejected, but retirement is not on the cards
"Obviously Massimo wants to continue," Roggi told the Calciomercato website.
"His preference would be overseas clubs, but if an offer did come in from an Italian side, we would not ignore it completely.
"At this moment we are in talks with West Ham, while we have already ruled out Major League Soccer."