The German club's general manager says the Reds are yet to make a concrete offer for the Greek defender, but admits that his side would consider a sale should a bid arrive.
The 21-year-old has been linked with a move to Anfield for months now, with recent reports suggesting that a deal somewhere in the region of 15 million euros is close to being concluded.
However, Heldt has claimed the Bundesliga outfit has yet to receive any offers for the promising Greek international, insisting his side is currently planning for the youngster's return from a devastating knee injury suffered in Nov. 2012.
"There's not a jot of truth in it," Heldt told German newspaper Reviersport. "We have no offer for Papadopoulos. Neither from Liverpool or some other club.
"On the contrary, we are very happy that 'Papa' is making progress and can be back soon, hopefully. We're planning with him."
Despite being adamant that no bid has arrived for Schalke's prized asset, Heldt did go on to reveal that the club will consider the sale of Papadopoulos should a sufficient offer be tabled.
He added: "If we receive an offer for him, we will come together and talk about that as we do with every player for us."