Both Germany internationals are being linked with returns to the Bundesliga as neither are regular starters for their respective clubs Chelsea and Arsenal.
Gelsenkirchen is not going to be a destination for either of them, though, with Heldt ruling his club out of the running.
“We’re not considering Andre Schurrle at all,” he said in Sport Bild magazine. “And the same goes for Xherdan Shaqiri and Lukas Podolski.”
Podolski has aired his frustration at not getting a regular game for Arsenal while on international duty for Germany, saying he will seek talks with the Gunners this winter.
However, Arsenal manager Arsene Wenger has ruled out a sale of the Germany international in January.
“It is not established at all that he will leave at Christmas,” Wenger told beIN Sports. “He is not for sale and there is no offer.”