The Greek centre-back has been linked with a move to the Italian giants, but Paul Koutsoliakos says that the 20-year-old is happy at the Royal Blues.
"The rumours are a strange one to me," he told Calciomercato.com. "He has only just signed until 2016 at Schalke.
"Maybe the clubs have contacted each other directly, but all I can say is that at the time of signing, Schalke and the player were completely satisfied.
"The boy is happy at the club and his family are entirely settled in Gelsenkirchen."
Papadopoulos joined Schalke from Olympiakos in 2010.