The German side's general manager admits Russian interest in the young Greek defender, who has also attracted the attention of AC Milan during this summer's transfer window
The 20-year-old has gained many admirers during his performances for Schalke, becoming a fan favourite along the way and also impressed whilst on international duty for Greece during Euro 2012.
"Zenit have contacted me," admitted Schalke general manager Horst Heldt.
"There is an offer, but whether it amounts to €13 million I cannot confirm."
Zenit coach Luciano Spalletti has already shown his intentions during this transfer window, stating his interest in Hulk, Nani and Ibrahim Afellay, but now looks to be attempting to add the young Greek player to his ranks too.
The Royal Blues won't be willing to let him leave easily but the Schalke chief believes Zenit have a strong desire to land the player.
"It's true, that they are interested and have made an offer. We don't want to let go of the player, but they are rather determined. So are we, though," Heldt insisted.