The Daily Star Sunday says the Spanish No.1 has been a fixture at the Bernabeu for years but his future is in doubt after spending much of this season injured or dropped.
And he hinted at a possible move in an interview earlier this week, saying: “I want the fans to remember me as a player who wore the Real shirt with pride.”
Casillas, 31, is under contract until 2015 but he has a frosty relationship with Jose Mourinho. He would cost the Gunners £17million.
Arsenal want a big-name star to come in and mentor gaffe-prone Wojciech Szczesny next season – and Casillas fits the bill.