The 57-year-old German footballing legend says he loves the way he goes about his work, adding that he wishes he was playing under him.
"I've seen the incredible energy Pep puts in," Rummenigge told the club's official website.
"It makes me want to go out there and join in myself! He has fantastic ideas, but he's also a meticulous hard worker. Nothing happens by chance, every last detail is planned."
Rummenigge also feels that, despite Bayern's incredible success under Jupp Heynckes last season, a change of coach is a good thing for the side.
"I'm utterly convinced we needed something new after last season. I've been through it myself, in 1975, 1976 and 2001. When you've had such great success, you're naturally inclined to take it a little easier - and that's an immediate step backwards," he added.
"It's no coincidence that we won nothing in 2001-02 and played nothing like the fantastic football of the previous season. But every player has to prove himself all over again for the new coach.
"Thanks to the high quality in the squad, none of them can take it easy. Any player who becomes complacent has a hungry man right behind him."
Rummenigge was also quick to praise new signing Thiago Alcantara, who joined from Barcelona for €20 million earlier in July.
"You can see he's a complete player," he continued. "He has exceptionally good technique, and he's completely taken on board our tactics, partly due to the fact he's already worked under Pep. I think we're going to get a lot out of Thiago."
Bayern saw off Barcelona 2-0 at the Allianz Arena on Wednesday night, thanks to goals from Philipp Lahm and Mario Mandzukic.