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.
