The 21-year-old has been in impressive form for the European champions of late and former Germany international believes he deserves a regular start for the club
The 21-year-old has been on an impressive recent run of form after initially struggling for fitness following his €37 million (£31.5m) summer move, and scored in the recent 3-0 win over his former club.
Rummenigge believes he is now worthy of a place in Pep Guardiola's starting XI, telling Sport Bild: "Gotze has been so playing so well that he definitely deserves to start more regularly now.
"He was brilliant against Dortmund, and I now feel he has properly made the big leap to Bayern Munich. He's added some extra pizzazz to the team."
Rummenigge was also quick to praise goalkeeper Manuel Neuer, and revealed he expects Germany to have Bastian Schweinsteiger in peak condition in time for the World Cup once he returns from injury.
"We love Manuel at the club, he is an incredible goalkleeper," he continued.
"He never, ever makes me feel nervous, even if he was to trip over on the ball in front of his goal.
"Schweinsteiger will be back for the second half of the season, and we hope he can inspire us to more trophy glory. He will be in the best possible condition when the World Cup next starts."