Bosz was speaking after Leverkusen advanced to the Europa League quarter-finals thanks to a 4-1 aggregate win over Rangers.
And Bosz said the club were doing all they can to protect Havertz before potentially selling him after their Europe run.
"We are watching all this closely," Bosz told DAZN and Goal. "Of 20 interview requests, 18 want to speak with Kai. Then we must make sure he doesn't go 18 times.
"He is an exceptional player, but even exceptional players can have a bad day. If we lose, he is always the first to be criticised, even if he didn't play that badly.
"I often talk to him and explain how I saw his game. Then there are games like the one against Hertha Berlin, when the fans whistled at his substitution.
"I told him that maybe he learned the most in that game, where he was really not good.
"But Kai is an intelligent boy overall and knows how the world works."