The official remained tight-lipped about rumoured interest in the former Barcelona coach, and assured the current boss that his job is safe, until Christmas at least
Heynckes' future with the club had been placed in doubt after finishing second in three competitions last season, and the former Barcelona boss has been linked with an early return from his year-long sabbatical to take the reins at the Allianz Arena.
But, speaking at Matthias Sammer's first press conference as the new Bayern sporting director, Rummenigge revealed that the club would not be rushed over the future of the current coach.
"We will think about it calmly," he told reporters. "You will get no quotes from us about this issue before Christmas.
"Only then will we sit down.
"Pep Guardiola? I have also read about this, but no one from Bayern has confirmed this."