Los GalÃƒÂ¡cticos currently trail league leaders Barca by two points having played 17 games, and travel to Athletic Bilbao on Saturday evening before Barcelona host Sevilla immediately after.
Speaking to Spanish newspaper Marca, Casillas outlined his belief that his side will overtake the reigning champions.
“I expect that we can win and Sevilla can beat Barcelona, thus making us leaders.”
“The San Mames will not be an easy place to go. They will be very motivated, the crowd will roar like lions.”
The 28-year-old went on to talk of his disappointment at the news that Gonzalo Higuain, who scored Real Madrid’s opening goal against Mallorca on Saturday, will be out of action for three weeks due to injury.
“It is unfortunate, [but] the good thing is that we have Benzema, Raul and Van Nistelrooy, although we keep suffering important injuries in difficult games.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news