The Bavarians defend a 2-1 lead in Wednesday's return clash in the Spanish capital, and the Bayern chairman is desperate to make it to the final of the competition at their own Allianz Arena.
"It's been a wonderful Champions League season for us so far. Reaching the semi-finals is already an achievement. Now we'll try and realise our fans’ greatest dream. It will take a night of Bavarian magic," Rummenigge said to reporters.
"A daunting task awaits us, but Mario Gomez’s last-minute goal has given us a small chance, which we'll try and take. We have some defending to do, but we want to get at them from time to time in attack, too. It's important we score.
"Reaching the final in our own stadium would be historic. No team has ever done it before, not even the greats like Barcelona and Real Madrid."
Wednesday's game at the Santiago Bernabeu kicks off at 20.45 CET.
Goal.com will be running a dedicated LIVE! on Wednesday from 15.00-00.00BST to keep you up to date with all the latest news, views and analysis on the second leg of the Champions League semi-final tie between Real Madrid and Bayern Munich.