Although the Gelsenkirchen outfit have reached the last 16 of the UEFA Champions League, inconsistent domestic form means they are seventh heading into the Bundesliga winter break.
Heldt has refused to back Keller, and a review of Schalke's entire operation will now be undertaken.
"Overall, it's been a turbulent half a year," Heldt told Sky Television.
"It's important that we draw our conclusions and realise what we've done well and what we've done badly.
"That means the work of every individual is examined, including the coaching team. We do this every six months as a rule.
"There have been situations that we've not been so happy with."
The latest setback for Schalke came in a 0-0 stalemate at Nuremberg on Saturday, a match Keller missed through illness.
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