Carlo Ancelotti's charges are in superb form, winning nine consecutive games across all competitions, and the Liga giants have not tasted defeat since losing 2-1 at rivals Barcelona on October 26.
The gap to leaders Barcelona and Atletico Madrid is now just one point, and Real are also primed for a UEFA Champions League quarter-final showdown with Schalke.
Real remain in contention for a Copa del Rey triumph, too, after Karim Benzema's strike ensured a 1-0 first-leg victory at Espanyol on Wednesday.
And Spain international Casillas is confident of mounting a challenge on all fronts.
"We have a chance in all three competitions and depend on ourselves and our own results," he said.
"We have made up a lot of points in La Liga, which is good for team morale.
"We have Schalke in the Champions League and we will take things a step at a time in the cup to try to make it to the final."
Casillas broke his personal record for the longest consecutive spell without conceding a goal when he reached 592 minutes in the victory over Espanyol.
The 32-year-old was thrilled with the achievement but also with the team's overall progression this term.
He added: "We did the necessary, which was to score and not concede. We had more chances to score. Now, back in Madrid, we'll try to seal our place in the semi-finals.
"I am pleased about the personal record and about how the team are doing as a whole because we are really focused, working hard and doing very well in defence."
