Real have fallen in the last 16 on each of their last five appearances in the competition, losing to Juventus, Arsenal, Bayern Munich, AS Roma and Liverpool last season, when they were humiliated 5-0 on aggregate.
With the Bernabeu hosting this season's final, Real, who won the last of their record nine titles in 2002, have an added incentive to do well.
"This team has the desire to do important things and all of us would like to get to the final, play and win, because it will be played in our stadium," midfielder Esteban Granero told the club's website.
Cristiano Ronaldo will expect to start at the Letzigrund stadium after being left on the bench for Saturday's Primera Liga trip to Espanyol.
The Portugal forward scored his second goal in as many league appearances after coming on as a substitute in the 3-0 win, although coach Manuel Pellegrini believes too much attention is being focused on him.
"I don't believe that Cristiano is carrying a weight on his shoulders. I think he is just under the microscope," Pellegrini said.
The Chilean also promised there would be room for everyone in a squad brimming with world-class players.
"The players who are picked know they have to do well and have to play a leading role in the game," he said. "Everyone is going to have an important role to play."
Defender Raul Albiol suffered a knock on his ankle against Espanyol but hopes to be fit. Sergio Ramos looks to be back to full fitness after three months out with tendonitis but Pellegrini is unlikely to risk him.
Swiss champions Zurich, semi-finalists twice in the days of the former European Cup, are making their first appearance in the Champions League group stage.
They warmed up with a 4-3 league win over local rivals Grasshoppers on Saturday.
The match has created huge interest and tickets sold out in 39 minutes at the club shop last week, angering fans who had queued for up to six hours.
However, little of this enthusiasm was evident when Zurich kicked off their campaign in front of only a few thousand fans against Maribor in the third qualifying round.
Teams:
FC Zurich: 1-Johnny Leoni; 13-Florian Stahel, 30-Hannu Tihinen, 19-Alain Rochat, 16-Philippe Koch; 7-Silvan Aegerter, 10-Onyekachi Okonkwo, 5-Xavier Margairaz; 8-Johan Vonlanthen, 12-Alexandre Alphonse; 29-Eric Hassli
Real Madrid: 1-Iker Casillas; 2-Alvaro Arbeloa, 18-Raul Albiol, 19-Ezequiel Garay, 12-Marcelo; 10-Lassana Diarra, 22-Xabi Alonso; 9-Cristiano Ronaldo, 7-Raul, 8-Kaka; 11-Karim Benzema.
