Ibrahimovic has accepted Milan's proposal and is ready to sign a deal to return to the former European giants within the next two days, Gazzetta Dello Sport and Sky Sports Italia reported.
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Ibrahimovic will reportedly sign a six-month contract worth about three million euros ($3.3 million) with a renewal option for another year, linked to certain conditions such as goals and appearances.
The 38-year-old striker confirmed his departure from Los Angeles Galaxy last month following the club's elimination from the Major League Soccer playoffs.
The Swede should be available to coach Stefano Pioli as early as December 30, the date of the resumption of training at Milanello.
AC Milan are reeling after a 5-0 thrashing against Atalanta last weekend, their worst defeat in 21 years, and are struggling 11th in the Serie A table.
The team's first game after the winter break will be at home against Sampdoria on January 6.
It is hoped that Ibrahimovic will bring some leadership and a winning mentality to the locker room.
Milan club manager Zvonimir Boban, a former midfield great with the club, slammed "an embarrassing performance" against Atalanta.
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"We will have to wake up and react. It will not be a good Christmas," said the Croatian.
Ibrahimovic played for two seasons between 2010 and 2012 with AC Milan, helping them to their last Serie A title, and scoring 42 goals in 61 league appearances.
He also won three league titles with Inter Milan, and two with Juventus, which were both revoked following the 'Calciopoli' match-fixing scandal.
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