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The Italian giants are keen to add some fresh blood to their squad following the departures of several first-team regulars, and they see the 25-year-old as a useful addition.
Drenthe was released on a free transfer by Real Madrid this summer after the Liga champions opted not to renew his contract, and the former Everton loanee has since been looking for a new club.
Milan face stiff competition in the race for the winger's signature though, as Manchester City, West Ham United and Dynamo Kiev have already contacted the player's agent to discuss a potential transfer.
Meanwhile, the Rossoneri have not given up hope of signing Real Madrid midfielder Kaka on a season-long loan deal.
The San Siro outfit lack the financial resources to pay a transfer fee for the attacking midfielder, but they remain hopeful that Madrid will allow Kaka to leave the club temporarily as the summer transfer window is set to slam shut in nine days time.
Milan are also keen on Lassana Diarra, but no movement is expected on his part until Madrid have wrapped up the signing of Luka Modric from Tottenham Hotspur.