Juve sports director Alessio Secco sees Kiessling as a potential long-term successor for David Trezeguet.
The youngster's agent, Ali Bulut, told TMW: "I know too about the interest of Juventus, but personally I have never been contacted.
"Are other clubs interested? Yes, there are many, but right now the player is comfortable in Leverkusen and in any case nothing will happen in the next window of the market. Hopefully we'll talk after the season ..."