The Dutchman is looking forward to the upcoming matches against his former team, and hopes to cause an upset versus the Blancos
The Netherlands international wore the Madrid jersey from 2007 until 2009, before leaving the club for Inter, and he still has fond memories of his spell with the Blancos.
"This is a tough draw, but it's a great one on an emotional level," Sneijder was quoted as saying by De Telegraaf.
"I was fortunate enough to win the Liga title in my first season with Real Madrid, and I still have warm feelings for Jose Mourinho, with whom I'm still in regular touch. Mourinho is very important to me, because I won the Champions League thanks to him.
"Real Madrid are obviously the favourites, but we will try to make life as difficult as possible for them. We might be able to spring a surprise."
The first leg of the quarter-final between Gala and Madrid takes place at the Santiago Bernabeu on April 3.