Sneijder had been handed an opportunity to return to the Santiago Bernabeu after Galatasaray were drawn against the Spanish giants, and the Dutch international is looking forward to facing Jose Mourinho, whom he played under at Inter Milan.
The 28-year-old told De Telegraaf: "This is a tough draw, but it's a great one on an emotional level.
"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."
Sneijder helped Galatasaray beat Schalke 04 in the last 16 of the Champions League earlier this week.