Milan confirmed that they rejected a £25m bid for the youngster last month, and the player himself claims that he was always going to stay at the club.
"I've always been convinced of my decisions, so I never thought about changing team," El Shaarawy told La Gazzetta dello Sport.
"I have been a Milan fan since childhood, so being here is a dream come true. I would never have left, not even faced with an offer from Real Madrid. I'd have said no to any team.
"I want to be here for a long time and write Milan history."
El Shaarawy joined Milan in the summer of 2011.