Kovac, who took over from Jupp Heynckes after leading Frankfurt to cup glory last season, has overseen a generational transition while keeping Bayern in the hunt for both domestic titles.
Yet he continues to face criticism from inside and outside the club, amid questions over his safety-first style and rumours that Bayern are eyeing Ajax coach Erik ten Hag and former Real Madrid boss Julen Lopetegui.
"Everything less than success is failure, I always knew that," said Kovac last week as he looked back on his first season in Munich.
Bayern can secure a seventh straight league title if they avoid defeat against Frankfurt, and could make it two trophies in a week in the German Cup final against RB Leipzig a week later.
Yet even a domestic double may not be enough to save Kovac, who appears to be the subject of a tug of war in the Bayern boardroom.
President Uli Hoeness has repeatedly backed his coach, stating early in the season that he would "defend him to the hilt", but CEO Karl-Heinz Rummenigge has always been cooler on Kovac.
"I am not a fan of job guarantees and I don't want to just praise the coach and the players," said Rummenigge after Saturday's 0-0 draw at RB Leipzig.
Later that evening, speculation over Kovac's future hit fever pitch when sporting director Hasan Salihamidzic refused to confirm whether the Croatian would still be in charge next season.
"Niko Kovac has my full support, but I can only speak for myself," he told public broadcaster ZDF.
Asked directly whether Kovac would hold on to his job, he replied: "we will see".
Kovac has faced the sack once before this season, after a draw at home to Fortuna Duesseldorf saw Bayern slip nine points behind Borussia Dortmund in November.
At that time, there were reports of dressing room disharmony over his training methods and rotation policy.
Kovac responded by rotating less, and led Bayern back into the title race with 13 wins in 14 games after the Duesseldorf debacle.
He also succeeded in integrating young players such as Serge Gnabry and Leon Goretzka into the first team.
Yet senior players have continued to criticise his style, which prioritises defensive stability.
"We played too defensively in both games and I don't know why," striker Robert Lewandowski told Norwegian television after Bayern were knocked out of the Champions League second round by Liverpool.
For all the promise of domestic success, the second round defeat to Liverpool continues to hang over Kovac.
On ZDF last Saturday, Salihamidzic singled the tie out as a low point of the season, saying that Bayern had "lacked courage" in the second leg.
Rummenigge, too, said in April that the Liverpool defeat had "rankled hugely".
"It did damage to us financially but also to our image, and to the image of the Bundesliga," he told Bild newspaper.
The defeat has certainly piled the pressure on Kovac to deliver the league and cup double, and the next two weeks may decide the fate of the Bayern coach.
"If we win the title, then I would rate this season a B+," said Salihamidzic on Saturday. "Otherwise, it was a turd of a season."