Keller was absent from the touchline during Saturday's 0-0 draw with Nurnberg due to illness, but the result which saw the Royal Blues drop to seventh in the Bundesliga standings at the midway stage of the season may mean he never gets to return to the bench.
The club's director of sport Horst Heldt refused to back his coach, instead admitting that a lot of events this season have not been to his liking.
"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."
Although Schalke have reached the last 16 of the Champions League, where they will face Real Madrid in February, they were eliminated from the DFB-Pokal by Hoffenheim and find themselves four points adrift of a place in the Champions League next season at the midway stage of the campaign.