The Spain goalkeeper is fit to train after recovering from a broken finger but will not feature against the Turkish team, having also been omitted for Saturday's 1-1 draw at Real Zaragoza in La Liga.
Mourinho, who according to media reports has a strained relationship with Casillas, named three goalkeepers for the first leg - Diego Lopez, bought in January as cover, and youth team products Antonio Adan and Jesus.
"[Casillas] is training well. He needs to carry on doing so and wait his opportunity," the Portuguese told a news conference at the Bernabeu on Tuesday.
Mourinho's assistant Aitor Karanka said last week Casillas lacked the "competitive edge" necessary to return to the team.
The former Chelsea and Inter Milan coach was pressed with more questions on Casillas but brushed them aside especially when asked about Real having not kept a clean sheet in their last seven games.
Mourinho pulled a note out of his pocket and read a series of statements made by the journalist who asked the question and accused him of not being impartial.
"There should be no law that says any particular player should play," Mourinho read out. "No one should play for what they have won in the past."
Looking ahead to Wednesday's tie, Mourinho was full of respect for a Galatasaray side many pundits say are the weakest team in the quarter-finals.
"They have a coach with experience in games at this level," Mourinho said of his opposite number, former AC Milan and Turkey boss Fatih Terim.
"They feel comfortable in games like this. He has no fear of playing here. He has people who have played in the greatest teams in the world.
"In Didier Drogba, Wesley Sneijder and Burak Yilmaz they have three players up front who can damage any side."
Mourinho has done a flurry of interviews in foreign media over the last few weeks and spoken warmly about his former clubs, prompting renewed media speculation on his future come the end of the season.
"I am not important, it's the results that are important," he said when asked whether he would be staying at Real beyond this campaign.
"Only the future of Real Madrid is important, not mine. I am trying to help the club achieve its objectives. We have two possible because the Spanish Super Cup is too small to satisfy a club like this," added Mourinho.
"We have a King's Cup final and a Champions League quarter-final where we will do the best we can. We'll try and finish in a manner satisfactory for this club.
"After the end of the season we'll see what is going to happen. I repeat again. The important thing is Real Madrid."
The news conference finished on a lighter note when Mourinho was asked about reports he provided Paris Saint-Germain coach Carlo Ancelotti with videos on how to beat Barcelona in their first leg on Tuesday.
"I had everything ready but I forgot to send it," said the Real coach.
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