The Bayer Leverkusen striker is seen as a potential replacement for Robert Lewandowski, hotly tipped to leave Dortmund this summer when he enters the final year of his current contract.
German international Kiessling's desire to stay with his current club comes hot on the heels of Schalke's Julian Draxler saying he would "never" join Dortmund.
Speculation in the German media has linked Draxler with a move since the announcement that Mario Gotze would leave Dortmund for Bayern Munich this summer, but Kiessling claims to know nothing about similar gossip surrounding him.
"I am not responsible for gossip rumours," the 29-year-old told Bild. "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's agent Ali Bulut rubbished the speculation in Kicker, saying: "Those rumours are pure nonsense.
"Stefan feels at home at Bayer Leverkusen, and we would talk at first to Bayer Leverkusen about everything."