The 32-year-old, who has made over 650 appearances for Real since 1999, lost his place to Diego Lopez under outgoing coach Jose Mourinho last season and has not yet featured in the Primera Division under new boss Carlo Ancelotti.
Casillas did, however, start against Galatasaray and FC Copenhagen in recent Champions League games and is happy to bide his time, as long as he is not ultimately shown the door at the Bernabeu.
He told Real's official website: "I would like to be at Real Madrid forever.
"It's the club I dreamed of being at when I was young and it's where I've had both my sporting and personal education."
Referring to Ancelotti's preference for former Sevilla keeper Lopez in league games, Casillas added: "These are the coach's decisions and all my colleagues are entitled to play.
"Players are selfish and want to be in the XI, but a good professional accepts decisions. I will fight every day to be in the team."
When asked if he would consider moving into coaching at the end of his playing career, he added: "I've not approached that idea yet.
"I think I would have to if I want to stay here. The main thing is that I keep enjoying the game and feeling like a footballer."
Los Blancos are currently third in La Liga, five points behind both Barcelona and city rivals Atletico Madrid, who claimed a rare 1-0 derby victory at the Bernabeu in late September.
"We are a different team from last year and the new coach and new players all need time to adapt, but we are on the right track," Casillas added.