The Tuscany-based side appear ready to grant their player the transfer he wants with a move to San Siro looking likely before the end of the summer transfer window
Montolivo, 26, has been linked with an exit after failing to sign a new deal beyond his current 2012 terms at the Artemio Franchi stadium.
"We have been clear with Montolivo. I asked his agent if he wanted to continue with us, but the response was that a decision has been made," Corvino told Sportmediaset.
"Having looked at Montolivo's will, we will now see what solutions the transfer market offers us. We only want motivated players for our future."
Last week Goal.com revealed how Fiorentina rejected a €6 million, plus Antonio Cassano, offer from Milan.
The Tuscany-based side are said to be asking for at least €10m cash plus the full rights to Cassano.
Milan coach Massiliano Allegri recently described Montolivo as a top player with bags of talent as his search for a midfielder to replace Andrea Pirlo continues.