Rummenigge wants Beckenbauer vigil at Bayern stadium
Beckenbauer, who was Germany's first truly global sports star and led them to the World Cup title as player and coach in 1974 and 1990 respectively, had become part of the country's social fabric in a hugely successful career on and off the pitch spanning over 50 years.
Beckenbauer, considered one of the best players of all-time, won 103 caps and captained West Germany to World Cup success in 1974, two years after lifting the European title.
He also headed the organising committee for the 2006 World Cup held in Germany.
"The whole world of football and beyond is grieving for our friend Franz," Rummenigge, who played alongside Beckenbauer at Bayern Munich in the 1970s, told Bild newspaper.
Rummenigge, a former longtime Bayern CEO, was West Germany's captain under coach Beckenbauer in the 1986 World Cup where they lost to Argentina in the final.
"As a thank you and in remembrance FC Bayern should organise a commemoration in the stadium which would not have existed without him," he said.
Beckenbauer was part of the mighty Bayern Munich team who won three consecutive European Cups from 1974-76 among other titles. He became the team coach and club president after his playing career, establishing the German champions as one of the most successful and valuable brands in European soccer.
The club, under the presidency of Beckenbauer, left the ageing Olympic stadium and moved to their purpose-built Allianz Arena in 2006.
A stadium ceremony is not the only proposal to remember the "Kaiser", a nickname he earned for his playing style and vision of the game.
Fellow 1974 World Cup winner Bertie Vogts suggested renaming the German Cup the Beckenbauer Cup to ensure his memory lives on.
"Maybe the German FA (DFB) should consider renaming for example the German Cup after Franz Beckenbauer," Vogts told the Rheinische Post newspaper.
"It is important that his name is not forgotten by the football generations that follow."