Kovac has been under increasing pressure of late, and reports earlier this week suggested that he would be shown the exit door even if he won a league and cup double this month.
Bayern immediately denied the rumour, and Kovac defiantly insisted that he would remain in his job on Saturday.
"I am convinced that I will continue," he told Sky, after being drenched in wheat beer during Bayern's customary title celebrations.
Asked about the report, he said he had "other, first-hand information", suggesting that he had been given a job guarantee by the Bayern hierarchy.
Bayern fans chanted Kovac's name as the clock ticked down on their title-winning victory on Saturday.
"That touched me, because I am a human being of flesh and blood," Kovac told Sky.
"I want to thank the whole crowd."
Bayern president Uli Hoeness said he had heard the chants, but refused to confirm whether Kovac would stay.
"I heard them, and they did me good," he told Sky.
"I have never involved myself in this discussion and I won't do so now on the day of our triumph."