The Bundesliga champions face Borussia Dortmund at Wembley on Saturday, and go into the game as favourites after easing to the German crown with a new record 91 points.
However, with the memory of the dramatic penalty shoot-out defeat to Chelsea in last year's final at their home stadium, Allianz Arena, still fresh in the mind, Rummenigge knows that the Bavarians cannot afford to be complacent.
"It's a final and we're not traveling to Wembley arrogantly or haughty," he said.
"We know what can happen in a final. We need a good day and we need to perform like we did in the most games in the last months. But we also know that we need a good day to reach our goals at the end of the day and get the Champions League trophy to Munich."
However, the Bayern chief was keen to stress that a European triumph would be a deserved one for manager Jupp Heynckes, who is managing in his last game for the club before Pep Guardiola takes over.
"I think our team showed great football over the last five years. We've been in the final twice, tomorrow is the third time," he added. 
"We're number two in the UEFA ranking, only Barcelona is still in front of us. I think that our team is very consistent this year and they played fantastic football. It's something special when you become champion with 25 points before the runner up. We've got a great coach and I think there's nobody in Germany who thinks this trainer does not deserve this title."
Saturday's contest will be the first-ever all-German UEFA Champions League final, and Rummenigge feels it would be even sweeter to win the trophy on English soil following last year's disappointment.
He explained: "Last year at May 19 we lost it very unluckily. Tomorrow our target is to bring the trophy to Munich. Last year an English team won in Munich, now we hope that a team from Munich can win the title in England."