The Allianz Arena CEO says that his side need to put in a good performance while fellow legend Lothar Matthaus is excited for the "spicy" all-German showpiece at Wembley
The Bavarians demolished Barcelona 7-0 on aggregate in the semi-finals, having dismantled Serie A champions Juventus in the last eight 4-0 over two legs, to be situated as favourites prior to the clash.
Domestically, die Roten also dominated - winning the Bundesliga by 25 points - but Rummenigge has said to his players that victory can only be guaranteed with a solid performance at Wembley.
The 57-year-old told reporters on Friday at Munich Airport: "It's a final. We must be neither arrogant nor cocky. We will need to have a good day and must play as we have in the last few months.
"We are desperate to win the trophy. Last year, an English team in Munich - now I hope that a Munich team can win in England."
Another iconic former Bayern star, Lothar Matthaus, believes the all-German aspect of the Wembley clash adds an extra element of excitement to the game and is predicting victory for Jupp Heynckes in his penultimate game as die Roten coach.
"We are very very happy to have two [German] teams in this final. We are proud of Bayern and Dortmund," he said to Sky Sports News on Saturday. "I hope first they are fully concentrated on the football. I hope they celebrate a great football game today - the fair play way, with high quality football.
"I wish [victory] to Bayern - sure they lost 2010 to Inter in Madrid, and last year in the final [to Chelsea] but I think that they will learn from the last two finals. They are favourites.
"Bayern played a great season, dominated Barca in the semi-finals. But it's the Champions League final. Playing against Borussia Dortmund will make it a bit more spicy.
"Franck Ribery is the main [threat], though Thomas Muller has played a fantastic season. He was playing a little bit below par but now he's played a brilliant season. I predict one of these two players will score the winning goal.
"[Heynckes] was my first coach at Borussia Monchengladbach, way back in 1979. I wish him all the luck this year."