Reports claim Galliani has taken the decision to step down after a breakdown in his relationship with Barbara Berlusconi.
Barbara Berlusconi, daughter of Silvio, recently publicly questioned the direction the club were heading in under Galliani's leadership, feeling Milan had under-performed in the transfer market in recent seasons.
Galliani has revealed he will step down from his role at the San Siro after next month's UEFA Champions League clash with Ajax.
"I will resign after the (Champions League) match against Ajax," Galliani told Ana news agency. "I quit for good reason.
"I understand a generational change but it should not be like that, I deserved more elegance. There has been a severe damage to my image.
"I will resign with or without agreement (on the severance pay).
"My future? I'll wait some time before deciding. My affection for president Berlusconi is not changed and it won't change."