This paper studies the thermodynamic properties, in particular the chemical potential, of a two-dimensional electron gas in superlattices of diluted magnetic semiconductors doped with manganese. Using the grand thermodynamic potential method, a general expression for the chemical potential is found. Based on this expression, taking into account the influence of the exchange interaction between conduction electrons and localized moment of Mn, the nondegenerate case of the electron gas is considered. It is found that in the nondegenerate case, the chemical potential is inversely proportional to temperature and depends logarithmically on carrier concentration. The exchange interaction modifies the chemical potential via the Brillouin function, an effect that is most pronounced at low temperatures and high magnetic fields.