Italian media report that Milan will be required to purchase Aquilani's full contract for ?6 million ($8.65 million) if he plays at least 25 matches this season.
Milan is prepared to pay Aquilani ?2 million ($2.9 million) this season and ?2.5 million ($3.6 million) the next two seasons - less than he was earning at Liverpool.
The 27-year-old Aquilani began his career with his hometown club Roma, then transferred to Liverpool for the 2009-10 season. He spent last season on loan with Juventus, and scored the winning goal when Italy beat World Cup-holder Spain in a friendly this month.
Milan has been looking for a midfielder to replace Andrea Pirlo.