Zenit St Petersburg have reportedly bid €15million (£12m) for Kyriakos Papadopoulos but Schalke do not want to sell.
The German club's sporting director, Horst Heldt, has confirmed an offer has been received from Zenit for the defender and the Russian champions are said to be 'very persistent'.
But Schalke are determined to keep one of the club's prized assets in Gelsenkirchen ahead of Friday's transfer deadline.
Heldt told Kicker: "They have made an offer and are being very persistent but we do not want to lose the player."
He was speaking after Schalke opened their Bundesliga campaign with a 2-2 draw at Hannover on Sunday.
Having overturned a 1-0 deficit to lead 2-1 with 10 minutes to go, the visitors were frustrated not to have taken all three points.
Midfielder Lewis Holtby, who grabbed Schalke's second goal after Klaas Jan Huntelaar had cancelled out Felipe's opener, said: "I am disappointed.
"We were clearly the better team and controlled the game, making plenty of opportunities. But we conceded two stupid goals."
Adrian Nikci grabbed the leveller for Hannover, whose coach, Mirko Slomka, was happy his side emerged with a share of the spoils.
"I am very happy with one point as it is a point gained," he told the club's official website.
"Schalke were very dominant in the second half and I am pleased we hit back after the setback of going behind."