Current Bayer coach Kasper Hjulmand has a deal to 2027 after being hired earlier this season.
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Leverkusen is in sixth place in the Bundesliga and is four points up from fourth place.
And Sky Deutschland states that Hjulmand is under pressure and risks being fired at the end of the season.
Bayer are now following German coach Hürzeler, 33, closely, as a potential replacement.
Hürzeler is high on the wish list if Bayer chooses to dump Hjulmand.