Mie resonances in dielectric particles can increase the local optical density of states (LDOS) associated with either electric or magnetic transition rates in nearby quantum emitters without ohmic losses. Their rather large quality factors compensate their low field confinement as compared to the plasmon resonances of metallic nanostructures for which nonradiative decay channels dominate. We show theoretically that near-infrared quadrupolar magnetic resonances in silicon particles can preferentially promotemagnetic versus electric radiative deexcitation in trivalent erbium ions at 1.54 μm. The distance dependent interaction between magnetic (electric) dipole emitters and induced magnetic or electric dipoles and quadrupoles is derived analytically and compared to quasiexact full-field calculations based on Mie theory. We discuss how near-field coupling between nearby particles can further enhance the magnetic LDOS and compensate for the weak refractive index contrasts between dielectric particles and a typical host matrix for the lanthanide ions.