The German giant, on the back of six successive Bundesliga titles, finds itself stuck in an uncharacteristic slump, goal.com reported.
A four-game winless run heading into the international break has Bayern sat sixth in the table, four points adrift of leader Borussia Dortmund.
Pressure has built on Kovac as a result, with calls for change on the field and in the dugout starting to mount in intensity.
Bayern fueled speculation regarding a possible managerial change just a few months after handing Kovac the reins after calling a press conference on Friday.
President Uli Hoeness, Chairman Karl-Heinz Rummenigge and sporting director Hasan Salihamidzic were all in attendance, with the announcement of Jupp Heynckes' return as coach taking place the last time those three joined forces at a media call.
Rather than announce a change in the dugout, though, the trio came out in defense of Kovac and hit out at his treatment in the German media.
Hoeness said, "I was accused of not publicly defending Niko Kovac. For that I have to clarify something. Why? We appreciate his work. We do not have to publicly back ourselves. This is disrespectful and outrageous, what happens here. This club will now unite in public again."
Salihamidzic added, "Niko knows we're behind him, it's outrageous what's going on here."
Rummenigge, meanwhile, took aim at the press, insisting that some of the reporting had been "sly" and "degrading". He said, "It is an important day for FC Bayern because we will not allow this degrading, sly factual reporting to continue. From today on we will protect our players, our coaches and also the club."
Those words will be music to Kovac's ears, with the Croat having held his own pre-match press conference on Friday in which he talked up the positivity and passion within his Bayern squad.
He said, "The fact is, the results are not right.
"In the first games, the number of scoring chances was the same as in the last four. The problem is that they were not converted.
"It was a good approach, but ball did not want to go in. We will not question everything and turn everything. We need that little bit of luck.
"The mood is positive. We also want and have to be positive. The passion is there.
"Life consists of failure and success. I can assure you that we have trained really well. Everyone desperately wants to play and win."
While Kovac is set to remain in his role for now, having penned a three-year contract upon his appointment, Wenger is among those to have been mooted as a possible successor if change is sought.
The experienced Frenchman has been out of work since bringing a 22-year reign at Arsenal to a close over the summer.
Wenger has been quizzed on the Bayern rumors and stopped short of ruling himself out of a future role in Bavaria.
He told Bild when discussing the current situation at Bayern, "It’s important that Hoeness and Rummenigge organize the transition.
"I think the power should stay within ex-players. People like Philipp Lahm and Oliver Kahn, it’s important that they take over. Football lives within you. You don’t learn that at university."
Wenger was, however, reluctant to add himself into contention for a position at Bayern if one becomes available, adding, "That’s not a topic for me. Uli Hoeness and Karl-Heinz Rummenigge trusted Niko Kovac and they have to hold on to him."