General manager Horst Heldt said that the club had yet to receive any offers for the Greek defender who joined the club three years ago aged just 18.
He has gone on to make 57 appearances for the Bundesliga club and break into his country's national side, winning 16 caps.
Newspaper reports are claiming that the 21-year-old is Brendan Rodgers' first choice to replace Napoli-bound Martin Skrtel, but Heldt claims they are in the dark.
"There is no truth in those rumours," he said, "there is no offer put up for the services of Kyriakos Papadopoulos. Not from Liverpool FC or any other club.
"In case we receive a written transfer offer for his services we would sit down and discuss that with him."
The former Olympiakos youngster has been out of action since November with a knee injury - something that is thought to be leading Liverpool to prefer an initial loan deal - but Heldt insisted Papadopoulos' recovery was on track.
He continued: "Papa is making good progress after his knee injuries and we hope to see him back fit soon. He is fully inside our future plans."