  We discuss a class of exact solutions of a three-parameter non-minimally
extended Einstein-Maxwell model, which are attributed to non-minimal magnetic
monopoles of the Dirac type. We focus on the investigation of the gravitational
field of Dirac monopoles for those models, for which the singularity at the
central point is hidden inside of an event horizon independently on the mass
and charge of the object. We obtained the relationships between the non-minimal
coupling constants, for which this requirement is satisfied. As explicit
examples, we consider in detail two one-parameter models: first, non-minimally
extended Reissner-Nordstr\"om model (for the magnetically charged monopole),
second, the Drummond-Hathrell model.
