Bayern have been linked with the 21-year-old winger several times in recent months and Transfermarkt claimed this week that they agreed personal terms after holding talks with his representatives over the weekend.
But Kovac felt compelled to silence talk of an imminent move, insisting there is no truth to the latest rumours.
"I am not responsible for transfers but I have to say something regarding this," he told reporters after his side's defeat to Tottenham in the Audi Cup final.
"I find it extraordinarily strange that you can blurt something out and nothing happens. You can just say something but it's not true.
"If you communicate something like this, there must be undeniable proof. Otherwise you cannot spread it as news.
"I would ask you to check it. It's not true, it's not verified. It's false."
Bailey, who joined Leverkusen from KRC Genk in 2017, has scored 17 times in 83 appearances for the German outfit and is tied to the club until 2023, having signed a new deal last August.
The Jamaica international is not the only winger Bayern have been reported to be trying to sign in the current transfer window.
The Munich club's president, Uli Hoeness, and CEO, Karl-Heinz Rummenigge, have been open about their desire to bring Leroy Sane back to Germany, despite Manchester City's attempts to tie him to a contract extension.
Kovac said recently that he is "very confident" of signing Sane this summer, though Rummenigge rebuked the coach for being overzealous, saying: "I did not like what he said.
“Sane still has a contract [at Man City]. Neither optimistic nor pessimistic quotes do anything to help us in that matter."
Kovac then backtracked on his comment, admitting that he had gone too far with his previous comment.
"We [Bayern and him] talked about it," he said. "Maybe I was too offensive in that interview. I talked to Pep and apologised because of it.
"I would like to apologise to the club, too. I will restrain myself in cases like this in the future."