The polarization-dependent photoluminescence of the negatively charged trion is investigated for ZnSe single quantum wells with varying quantum well thickness between 5 and 20nm and barrier heights ranging from 30 to 200 meV under application of magnetic fields up to 10 T perpendicular to the quantum well plane. A strong increase of the trion binding energy with decreasing quantum well thickness from about 2.5 to 7 meV is observed. For the trion spin-singlet state the stabilization with increasing magnetic field is found to be negligible. Under high magnetic fields (B > 6 T) a shoulder emerges on the low-energy side of the 1 s heavy-hole exciton resonance which is attributed to the excited trion spin-triplet state becoming stabilized in high magnetic fields.