The 42-year-old has reiterated his desire to keep the Greece international at the club, and discussed the contractual situation of Klaas-Jan Huntelaar
Goal.com exclusively revealed on Friday that the Rossoneri wanted to sign the Greece international as a replacement for Thiago Silva, who left the Italian club to join Paris Saint-Germain on Saturday, but Heldt is determined to keep the 20-year-old in Gelsenkirchen.
"AC Milan have expressed an interest in Papadopoulos, but he is very happy at Schalke, however, so the matter is closed," the club official said at a press conference.
The 42-year old went on to confirmed that the Bundesliga club will soon enter negotiations with Klaas-Jan Huntelaar, Atsuto Uchida and Lars Unnerstall over new contracts.
"We will talk with Huntelaar. I know what he wants. He will stay next season if nothing happens. Klaas-Jan Huntelaar has clear opinions, and it's good that way.
"We have the same goal, we want to play in the Champions League again. I can't answer the question if he will extend his contract. But I'm optimistic.
"We are sticking to our goal of reducing the size of the squad. New signings can never be ruled out but none are planned.
"And we're deep into contract talks with Unnerstall and Uchida."
One Konigsblauen star to have been linked with a move away from the Veltins Arena is Lewis Holtby, who recently admitted that he would be tempted by a switch to the Premier League.
However, Heldt is confident that the 21-year-old is fully committed to his current employers, and is eager to make his mark on the first team.
"Holtby is showing himself to be very dedicated. He wants to defend his place in the team."