Balotelli, 30, who has been without a club since leaving Brescia this summer, trained with Serie D side Franciacorta in November.
Monza, who have ex-Tottenham midfielder Kevin Prince-Boateng in their squad, are ninth in the table.
During his time at Inter Milan Balotelli won the Champions League, three Serie A titles, the Coppa Italia and Italian Super Cup.
He found the back of the net 28 times in 86 appearances for the Nerrazurri.
And at Manchester City he won the Premier League and FA Cup scoring 30 goals in 80 matches.
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