The 31-year-old goalkeeper has made just two appearances for the Rossoneri this season and claims he has "with great regret" asked CEO Adriano Galliani to arrange a transfer
The 31-year-old has featured just once in the Champions League for the struggling San Siro outfit this season, slipping behind Christian Abbiati and Gabriel in the pecking order under Massimiliano Allegri.
And his continued omission appears to have driven Amelia to the exit door after he revealed on Twitter that he had spoken to club CEO Adriano Galliani about securing a transfer from the Rossoneri.
He posted: "I asked to Dr. Galliani to let me go away, with great regret, but after the last few months is the best solution for everybody!"
Amelia, who joined the club permanently from Genoa in 2011, has a contract with Milan until June 2015.
Milan currently sit in 11th place in the Serie A table, 27 points adrift of leaders Juventus.