The 31-year-old has featured just twice for the struggling San Siro outfit this season, but has not made a single Serie A appearance, with Christian Abbiati preferred between the posts.
And his continued omission appears to have driven Amelia to the exit door, revealing on Twitter that he had spoken to club vice-president Adriano Galliano about securing a move away.
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!"
Milan currently sit 11th in Serie A, 27 points adrift of leaders Juventus.
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'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
