Wenger had been seen as the favourite to replace Niko Kovac, who was sacked last weekend.
However, Rummenigge, speaking after a 4-0 hammering of rivals Borussia Dortmund, said Flick will be in charge “until further notice”.
Rummenigge, however, confirmed he would look to contact Wenger, who had claimed the Bayern chief sought him out.
“I have respect for Arsene. We will call and clear things up. I don’t want to have stress with him,” he said.