The Parma defender's agent has confirmed the deal is likely to go through on Friday, after the players have completed medicals at their respective new clubs
The 31-year-old full-back had been linked with a switch to San Siro earlier in the transfer window, but the deal fell through as both parties failed to agree to the length of the contract.
However, the right-back's agent has confirmed he is poised to seal a move to the Rossoneri, with Algeria international Mesbah expected to move the other way.
“Milan is a great opportunity for Zaccardo and a real high point in his career,” Alessandro Moggi told La Gazzetta dello Sport.
“His contract will be to June 2017, as Milan have bought out the existing deal from Parma. Zaccardo hasn’t given up on anything.”
The deal is likely to fuel speculation over the future of Ignazio Abate, who has been linked with a move to Russian side Zenit St Petersburg.
Meanwhile, Steffano Sorentino is poised to seal a switch from Chievo to Palermo, with a €4 million transfer also expected to be confirmed on Friday.