General manager Horst Heldt stated that Schalke 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 has broken into his country's national side, winning 16 caps.
Newspaper reports have claimed that the 21-year-old is Liverpool manager Brendan Rodgers' first choice to replace reported Napoli target Martin Skrtel, but Heldt says they are in the dark.
"There is no truth in those rumours," he told Reviersport. "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 reported 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."