The Bayern CEO has demanded that Germany lift a trophy for the first time since the 1996 European Championship following the success of Jupp Heynckes' side and Borussia Dortmund
The Bavarians and Borussia Dortmund clashed in the Champions League final this campaign and an increasing number of football fans are following German football, which is praised for its low-price season tickets in particular.
Since West Germany and East Germany rejoined, the side are yet to add to their World Cups in 1954, 1974 and 1990 - a fact that former Mannschaft star Rummenigge wants erasing.
"Dortmund and Bayern have many Germany internationals and got to the Champions League final - this is proof that a national team trophy is possible," the 57-year-old told Bild.
"There is no point in talking in understatement - next year, this generation must achieve the ultimate goal of World Cup victory after 18 years [since Euro 1996 success], Germany can expect to have a title finally ..."
Joachim Low's men face USA on Sunday in a friendly match following their 4-2 victory over Ecuador in midweek.
The country currently sit top of Group C in qualification for next summer's World Cup in Brazil.