We discuss quantization of semisimple conjugacy classes of simple com-plex algebraic groups via quasi/pseudo parabolic Verma modules. Such modules can be associated with points on a fixed maximal torus. When the points lie on the same orbit of the Weyl group, their conjugacy classes coincide. Although the isotropy subgroups are isomorphic in that case, their polarizations, in general, do not perfectly match the polarization of the total group. Namely, their basis of simple roots may not be a part of the total basis. With respect to this criterion, we classify the stabilizers as of Levi, quasi-Levi (isomorphic to Levi), and pseudo-Levi (essentially non-Levi) types. Accordingly, we consider parabolic, quasi-parabolic, and pseudo-parabolic modules of highest weight and ask if they support quantization of conjugacy classes (exact representation of the quantized coordinate ring). The answer is positive for the special linear group. It seems that there are limitations on the points for other types of quantum groups. This subject is under study.