The Rossoneri see the Spaniard as a perfect long-term replacement for Christian Abbiati, who is nearing the closing stage of his career.
They are well aware of the player’s desire to take part at the 2014 World Cup and are prepared to guarantee him regular playing time at San Siro.
Sport has suggested that Milan have already opened talks with Casillas’ agent, with a view of signing the Spain international in January.
The 32-year-old is unhappy at playing second fiddle to Diego Lopez and he is eager to leave los Blancos at the earliest opportunity.
Casillas is expected to make his second appearance of the season in the Champions League clash against FC Copenhagen on Wednesday.
Real Madrid are clear favourites to defeat the Danish side, with Casillas 8/11 to keep a clean sheet.