The Italian's agent has revealed that the Serie A champions have initiated talks for his client, while defending the player's choice to put contractual talks on hold
Montolivo's future in Florence has been a major discussion point, after the midfielder refused to sign a new contract with the club at the end of the last season.
The 26-year-old, whose current deal expires next summer, has been linked with moves to AC Milan, Inter and Juventus, though the Scudetto holders are thought to be frontrunners in the race to sign the midfielder.
Adriano Galliani, vice-president of the San Siro outfit, admitted last month the club could sign Montolivo, and the representative of the Italy international believes negotiations between the two sides have already taken place.
"I think Milan have talked to Fiorentina; we will only talk when Fiorentina have reached an agreement," Giovanni Branchini told Gazzetta dello Sport.
"[A transfer to Milan] is a decision that belongs only to Fiorentina."
Branchini has defended Montolivo, who has come under fire for his decision to reject talks over a new deal.
"I want to make it clear that the right not to extend a contract is the same for a player and for a club," he noted.
"Throughout Europe and in the world, a footballer plays until the last day of his contract with the maximum commitment, without being the subject of a soap opera, which unfortunately has been the case in Florence.
"Montolivo has not asked to be transferred, nor has he put pressure to be transferred to this or that club, despite what has been written in these suspicious times."