It had been suggested that the 29-year-old would replace Robert Lewandowski, who looks certain to leave the Champions League finalists at the end of the season.
However, Kiessling told Bild: "I am not responsible for gossip rumours. I have been in touch with nobody. I am under contract with Bayer Leverkusen until June 2015.
"Thus far I have not had any conversation with someone from the club, and I feel the club should come to me.
"I am not under pressure, I like being at Bayer Leverkusen and everybody knows that. I could definitely imagine signing a new deal, of course."
Kiessling has scored 24 goals for Leverkusen this season.