Let $K$ be the complex line bundle where the Kostant-Souriau geometric quantization operators are defined. We discuss possible prolongations of these operators to the linear superspace of the $K$-valued differential forms, such that the Poisson bracket is represented by the supercommutator of the corresponding operators. We also discuss the possibility to obtain such super-geometric quantizations by (anti)Hermitian operators on a Hilbert superspace. We apply our general considerations to Kahler manifolds and to cotangent bundles of Riemannian manifolds.