The flashpoint comes as a result of the decision to take Angelos Charisteas and Ali Karimi to the Veltins Arena last month, which caused a protest by fans.
With 11th-placed Schalke suffering a disappointing campaign in the wake of finishing as runners-up last season, it was expected that Magath would use January to invigorate his squad.
But the club's chairman, Clemens Tonnies, does not think that the free signings of striker Charisteas, 30, and midfielder Karimi, 32, represent inspirational work.
Tonnies told Sport1 media: "Schalke has a huge fan base and you need to give the people a lift when deciding something.
Respectable
"I feel he (Magath) has missed out on that. This is why he appeared to end up criticised, kind of self-inflicted."
Schalke earned a respectable 0-0 draw with bitter derby rivals and Bundesliga leaders Borussia Dortmund on Friday night, thanks largely to the heroics of goalkeeper Manuel Neuer.
The point was secured without the services of former Mainz captain Tim Hoogland, who was close to returning from a back muscle injury but is now likely to miss the rest of the season due to knee surgery.
Magath told KICKER: "Tim Hoogland's knee looked swollen on a couple of occasions. This is why we felt knee surgery would be best in his case.
"During the surgery the doctors have removed a joint cartilage. The recovery process will probably sideline Tim Hoogland for some time, most likely for the rest of the season."