The French forward, who moved to the Rossoneri in 2014, ended his first season as the club's top scorer, with 34 appearances and 16 goals in all competitions.
However, injuries restricted him to just 10 Serie A appearances last season for the San Siro outfit.
"FC Girondins de Bordeaux have reached an agreement with AC Milan for Jeremy Menez," read a statement on the club's official website.
"Subject to a medical, the French international will sign with Les Girondins before being presented to the Press on Monday afternoon at Chateau du Haillan."
The 29-year-old, who has won 24 caps for Les Bleus, counts Paris Saint-Germain, Roma, AS Monaco and Sochaux among his former clubs.