A number of supporters and pundits have written off Jose Mourinho's side in the race for the Primera Liga title, after a poor start to the season has seen them fall 11 points behind Barcelona.
But goalkeeper Casillas admitted that he would give their fierce rivals a landslide victory in La liga if they were assured of La Decima.
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Mourinho is currently preparing his side for their Copa del Rey round of 16 match against Celta Vigo on Wednesday, and assistant coach Aitor Karanka denied that the club have only one priority and that they will be doing all they can to win all the competitions they take part in.
"Is the priority the cup or the league? At this club, and for its coaching staff, the priorities are all titles and all matches," he told a press conference.
"The cup match has no less priority than any other match."
The former Athletic Bilbao defender also revealed that Los Blancos are doing all they can to close the gap at the top of the league as they aim to win back-to-back titles for the first time since 2008.
He added: "We do not think like Casillas. The coaching staff are already quite uncomfortable with the gap and we do not want to be further behind. Here you fight for every title, and so we will continue addressing it."