Sporting director Leonardo is also reportedly set to quit because of differences with Ivan Gazidis, the administrator brought in by US hedge fund Elliot Management which bought the club last year.
Faced with mounting debts and threatened with FIFA sanctions for breaking financial regulations, AC Milan are adopting spending curbs and seeking to boost their coffers by buying young, unproven, talents who they hope to sell later for a profit, according to several media reports.
Gattuso, whose contract ends in 2021, was a controversial appointment in November 2017, but has won admirers despite failing to qualify the club for next season's Champions League, finishing one point behind Inter in the battle for the third and final qualifying spot.