The Spain international goalkeeper has had a trophy-laden career with the Bernabeu outfit, and counts five La Liga titles, a Copa del Rey medal and two Champions League triumphs on his impressive resume.
But Real have never completed the treble in their illustrious history and Casillas is keen to buck that trend by collecting a clean-sweep of trophies as his side strive for their 10th European crown.
"I'd like the last piece of news for this season to say that Real Madrid had won the treble," he said in an interview with Bwin. "That on May 24, Real Madrid won the first treble in its history.
"We know it is difficult because there are other teams that also want to win titles. But we are where we want to be right now, which is fighting in all three competitions.
"I hope the headline we see on May 25 reads that Real Madrid has won every possible title."
Madrid continue their quest for a first Champions League triumph since 2002 in the last-16 first-leg tie against Schalke on Wednesday and Casillas is expecting a tough encounter, particularly from former Real forward Klaas-Jan Huntelaar.
"They are a German team, a side that is physically strong," continued the 32-year-old. "They are improving in the Bundesliga and after a shaky start they are up in the top four.
"They have one player, Huntelaar, who recently recovered from a serious injury, and I think they are dangerous rivals.
"We are solid in attack, with decisive players who are in good form and that has to be our style: to maintain the defensive line with the help of the rest of the team, while trying to score a goal ourselves in every chance that we get."