Matri rejoined Milan, the club where he started his career, last summer from Juventus for 11 million euros.
The 26-year-old striker has endured a difficult spell with the Rossoneri, scoring once in 15 Serie A appearances.
"Matri will undergo a medical with Fiorentina and it will be (Giampaolo) Pazzini to lead the attack against Spezia (in the Coppa Italia) tomorrow," AC Milan interim coach Mauro Tassotti said in Tuesday's press conference.
Fiorentina are desperately looking to strengthen their attacking line with top summer signings Mario Gomez and Giuseppe Rossi both out with knee injuries.
Matri could make his debut with the Tuscan outfit at bottom-side Catania on Sunday.