Los Blancos are yet to suffer defeat in 2015-16 and the Spanish goalkeeper wants the run to continue as they challenge on multiple fronts
Rafael Benitez is yet to taste defeat in the 14 matches in all competitions he has presided over since taking the helm.
But despite their great start to the campaign, Madrid only sit top of the table on goal difference with Barcelona – who suffered defeat a 2-1 loss at Sevilla in October - matching their 24 points.
Casilla knows that trips to the Ramon Sanchez Pizjuan are frequently tough, but is keen for his side to maintain their current form on all fronts.
"The next game against Sevilla will be really difficult, but we know that we must give everything to maintain this run of results," the goalkeeper said.
"Real Madrid is the best side in the world. We know that we always have to win and that motivates us to be at our top level.
"Our aim is to compete for everything. We are on the right path and everyone in the dressing room wants the run to continue."
The 29-year-old has made just one league appearance so far this season – coming in the 3-1 defeat to Las Palmas – but could be in line to start once more with Keylor Navas struggling with a groin injury aggravated against Paris Saint-Germain in midweek.
Marcelo (thigh) and Karim Benzema are also doubts, with the striker charged with complicity in an attempt to blackmail and participating in a criminal conspiracy as part of an investigation into an alleged sex-tape plot involving France team-mate Mathieu Valbuena this week.
However, the returns of Gareth Bale and Dani Carvajal to training on Thursday will provide Benitez with a boost, while Pepe could make his first appearance since September.
Sevilla boss Unai Emery was pleased to have Ever Banega available for the 3-1 Champions League defeat to Manchester City following an ankle injury.
While he insists his team are not reliant on the Argentina midfielder, he wants other members of his squad to step up when called upon and provide strength in depth.
"We won at Barcelona without Banega, although it was said that the team didn't know how to win without him," Emery said.
"Banega gives a different touch, but, for example, [Michael] Krohn-Dehli is a great player who perhaps hasn't given his best level for Sevilla.
"We must unite to have two players per position – we cannot depend on one player."
Sevilla – who recently tied Grzegorz Krychowiak to a new contract that will run until 2019 – were beaten 3-2 by Real Madrid in this fixture last season.
Cristiano Ronaldo scored his fifth hat-trick against the Andalusian side in that game, taking his Liga tally against them to 19 – more than he has scored against any other top-flight club.
- Sevilla could become the first team to win Barcelona and Real Madrid in La Liga this season.
- Real Madrid won all games in Nervión that they played there last season something no other side managed to do.
- Rafa Benítez won his last league title at Sánchez Pizjuán in Spain (with Valencia on 2004).
- Since December 2011, two Madrid wins against Sevilla have always been followed by a Sevilla win.
- Real Madrid became the final team to concede a first half goal in the top five European leagues this season when they shipped a goal against Las Palmas in their last match.
- Cristiano Ronaldo has scored more La Liga goals against Sevilla than versus any other side (19).
- Cristiano Ronaldo has five hat-tricks against Sevilla – more than against any other side in all competitions with Real Madrid. He has scored 10 goals in his last five La Liga games in Sevilla.
- Sevilla have conceded a goal in eight of their last nine La Liga games (14 goals in total).