Rossoneri caretaker coach Mauro Tassotti has revealed the striker is set to move to la Viola on loan until the end of the season
Matri, who has scored just one goal in 18 appearances in all competitions this season, has found chances limited at the San Siro since he joined from Juventus in the summer.
Fiorentina lost forward Giuseppe Rossi to a knee injury earlier in January and coach Vincenzo Montella has moved swiftly to secure a deal for Matri in order to provide cover in attack.
"Matri will undergo medical tests at Fiorentina," Tassotti told reporters ahead of Milan's Coppa Italia quarter-final against Spezia on Wednesday.
"[Andrea] Petagna has returned and we have [Giampaolo] Pazzini back tomorrow. [Milan] are well covered in attack."
The former Italy international also wished new boss Clarence Seedorf well after the Dutchman was appointed as Massimiliano Allegri's replacement at San Siro, and voiced his confidence that the ex-Rossoneri midfielder can help restore the club to the summit of Italian football.
"I hope that there is a change of mentality and a return to the old values," said Tassotti. "I hope we can realise that this hypothesis is right - there are great players who can be great coaches.
"Certainly, Clarence has the right personality and I'm curious to see how it will work out."