Leipzig had previously been unbeaten in their maiden top-flight campaign, but fell to a 1-0 defeat at lowly Ingolstadt, whose Bavarian neighbours Bayern thrashed Wolfsburg 5-0 to take pole position on goal difference.
And Rummenigge now wants to reward Ingolstadt - who moved off the bottom with victory - for their efforts.
"Now they can have a cartload of sausages and beer from Munich, then they can support us at a distance," he said.
"Anyone who has such neighbours cannot complain."
Bayern will hope to return the favour at Darmstadt - who are a a point behind Ingolstadt at the bottom - next week, before facing Leipzig in their final match prior to the mid-season break.