In his first Bundesliga match in interim charge of the first team, Flick watched his side dispatch Dortmund in clinical fashion at the Allianz Arena on Saturday.
Two goals from Robert Lewandowski, one from Serge Gnabry and an own goal from Mats Hummels made it two wins from two for Bayern this week following a 2-0 Champions League defeat of Olympiacos on Wednesday.
Bayern have been linked with Erik ten Hag, Massimiliano Allegri, Jose Mourinho and Arsene Wenger in their search for a full-time successor for Niko Kovac, with Wenger stating on Friday that he expects to hold talks with chairman Rummenigge next week.
However, it seems Flick will stay in charge for the time being, with Rummenigge telling Sky: "We will continue with Flick until further notice."
When asked if Flick would be in the role for the Bundesliga match at Fortuna Dusseldorf on November 23, Rummenigge replied: "You can expect that."
Wenger said this week that he would not turn down the chance to speak with a club of Bayern's stature, having spent more than a year out of management since leaving Arsenal at the end of the 2017-18 season.
"It's nice to let me explain the story because it's a surprising story," Wenger told BeInSport.
"First of all, I don't have any agent. I am the only one involved in this story. Nobody can talk on my behalf.
"Secondly, I've known [Franz] Beckenbauer, Rummenigge and [Uli] Hoeness for 40 years. The success of this club has been built on its exceptional competency, honesty, discretion and simplicity. We always told the truth between all of us when necessary.
"What happened? My name came out of nowhere, without having anything to do with this. On Wednesday afternoon, Rummenigge called me.
“I could not answer at that moment, and by politeness, I called him back. He was in his car going to the game against Olympiacos.”
Bayern's thumping win against Dortmund helped to keep up their bid to win an eighth successive Bundesliga title.