Arsenal tried to land the 20-year-old Germany international in January, but Schalke stood firm in wanting to keep the young forward.
It was expected that Arsenal would return in the summer for Draxler, who has also been strongly linked with Bayern Munich, although Karl-Heinz Rummenigge has stated they will not be bidding this summer.
Draxler has four years left on his current deal with Schalke, and his release clause of over £35million would need to be met in order to prise him away, but Heldt is confident he will stay put.
General manager Heldt told Sky Deutschland: "I definitely believe that he will be staying at our club for the new season.
"Julian (Draxler) is an important player in our squad, he is playing regular matches and he is doing quite well."
Meanwhile, Draxler himself has played down a spat with coach Jens Keller during the weekend's win over Hertha Berlin.
"We had contrasting views on a certain situation and had a discussion. We came to the conclusion that I was right [laughs]. No, we had a misunderstanding, but it was nothing serious."
Keller added: "It was about running paths...we discussed it and Julian was right. Empowered players are no problem for me. "