The Gala boss believes his side's "world class" supporters can help the club inflict a home defeat on los Blancos for a second time in successive European campaigns
Gala reached the quarter-finals of the competition last term, where los Blancos eliminated them 5-3 on aggregate over two legs.
But the Turkish giants won the second leg at home 3-2 and Terim believes his men can once again spring a suprise on Carlo Ancelotti's star-studded side.
"Real Madrid are the favorites of this group," Terim said.
"One of the two best players in the world is [Cristiano] Ronaldo. The newcomer [Gareth] Bale, same. [Angel] Di Maria, [Karim] Benzema, [Sergio] Ramos, [Iker] Casillas... There are plenty of them.
"They are very strong. But what we say is that we want to succeed in Ali Sami Yen Arena."
Gala will have the backing of their famous home support on Tuesday and Terim is convinced the club's "world class" supporters can give them a crucial edge.
"We can compete against any team," the 60-year-old told a press conference.
"The will, the heart is important. When the Galatasaray team meet with the supporters, everybody knows what my players can do.
"No one should expect a Galatasaray that will accept defeat - especially in European cups. You may not see me to speak like this in Turkey. But in Europe, this is the case.
"We respect our opponents. But we expect the same thing from them too."
"Our supporters are world class. They will have an important mission. I ask their support for our players. We all are Galatasaray fans."