Germany's two top clubs have made attempts to calm tension between each other in recent months, with the Bavarians' recent deals to sign BVB stars Mario Gotze and Robert Lewandowski having created animosity.
However, Rummenigge has been speaking openly about the possibility of Bayern attempting to lure Marco Reus away from Signal Iduna Park over the summer, much to Watzke's annoyance.
"Our relationship has been professional for a long time but, at the moment, I believe there's no relationship at all," he told SportBild.
"You shouldn't talk publicly about contractual terms of employees of a competing company to the public, no matter how you say it, and the Bundesliga is no exception.
"Nobody in Germany speculated about whether Toni Kroos was going to Real Madrid because it wasn't their business..."
Bayern and Dortmund will renew on-field hostilities at on Wednesday evening, when they clash in the DFL-Supercup at Signal Iduna Park.