Kovac steered the German giant to a seventh consecutive league title on Sunday (AEST) after a 5-1 win over his former club Eintracht Frankfurt.
His position has come under intense speculation throughout the season, with suggestions that he could still lose his job even if he secures a domestic double in next weekend's DFB-Pokal final against RB Leipzig.
But Kovac remains defiant and insists he will still be in charge at the club for the 2019/2020 campaign.
"I have information in the background, and I am convinced that I will continue," he said.
Asked if the club has told him that he would definitely be Bayern coach next season, Kovac smiled and said: "Yes, we'll put it that way."
Supporters chanted Kovac's name after the game, and the visibly moved 47-year-old added: "Of course it touches you.
"I'm made of flesh and blood like everyone else. The fans have a good feeling for what we've done."