The 29-year-old, who has six caps to his name for Germany, has been hotly tipped as Robert Lewandowski's potential replacement should the Poland international leave BVB at the end of the current campaign.
Kiessling has played down the rumours, however and insisted that he is happy at the current third-placed side in the Bundesliga.
"I am not responsible for gossip and rumours. I have been in touch with nobody," Kiessling told Bild.
"I am under contract with Bayer Leverkusen until June 2015. Thus far I have not had any conversation with someone from the club as 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's agent Ali Bulut also played down the rumours that his will player will leave his current club and says that any discussion with other teams would be subsequent to talks with Leverkusen.
"Those rumours are pure nonsense," he told Kicker.
"Stefan feels at home at Bayer Leverkusen and we would talk at first to Bayer Leverkusen about everything."
The German has scored 24 goals in 40 appearances for Leverkusen this season, and trails Lewandowski by one goal in the battle to be Bundesliga top scorer this season.