  We discuss certain generalization of the Hilbert space of states in
noncommutaive quantum mechanics that, as we show, introduces magnetic monopoles
into the theory. Such generalization arises very naturally in the considered
model, but can be easily reproduced in ordinary quantum mechanics as well. This
approach offers a different viewpoint on the Dirac quantization condition and
other important relations for magnetic monopoles. We focus mostly on the
kinematic structure of the theory, but investigate also a dynamical problem
(with the Coulomb potential).
