The midfielder was expected to leave the San Siro outfit during the season break with his current deal ending next month.
However, the 28-year-old has reportedly agreed to reduce his wages by half in order to remain with the Rossoneri.
The former Arsenal midfielder joined Milan in 2008 but missed most of last season with a serious knee injury.
Flamini's decision to stay could end Milan's pursuit of
Earlier this week, Milan claimed it had not ruled out the possibility of signing Aquilani, who is considered the ideal replacement for Flamini.
Aquilani played on loan at Milan last season and scored one goal in 23 league appearances.
The 27-year-old is under contract with the English Premier League side until
Socceroos midfielder Carl Valeri will play Serie A football for the first time after Sassuolo claimed a maiden Serie B title with a 1-0 victory over third place Livorno.