The Gelsenkirchen side are short defensively and, with key centre-back Kyriakos Papadopoulos out of action through injury, the Champions League-chasing side may well opt to bolster their ranks in the January transfer window.
Heldt admitted that no contact has yet been made with their Bundesliga rivals, but admitted Kirchhoff is on their radar, with his current deal set to expire this coming summer.
"This [Kirchhoff] is an interesting player, whose contract expires at the end of the season," the club's chief said to Reviersport.
"We have contacted his agent because he has some of our players under contract.
“Currently we have had no contact with Mainz, but the fact is that through the even longer injury-induced loss of Kyriakos Papadopoulo, we need cover in the centre of defence."
Schalke currently sit seventh in Germany's top flight - 17 points behind leaders Bayern Munich - a deficit that resulted in the sacking of coach Huub Stevens 10 days ago.