The Italian international joined AC Milan on a free transfer in the summer, bringing a seven-year stint with Viola to an end.
He is likely to face his former club when the two sides meet at the San Siro on Sunday, but it is uncertain what sort of reaction he will get from the Florence faithful.
However, Rossi - who was sacked in May - believes that the fans should give the midfielder a warm reception, as he continued to give his best despite heading for the exit door.
"Riccardo is a great professional," Rossi told Firenze Viola.
"I did not like the situation that had surrounded him, but I kept picking him because he has great feelings for Fiorentina.
"He was always a leader in the dressing room, it was just some details on his contract that kept him from staying."
Montolivo has won 39 caps for Italy.