The spectrum of gravito-acoustic modes is depleted in dipolar modes for a significant fraction of the giant stars observed by Kepler, a feature that can be explained by the presence of magnetic fields in the core of these stars (Fuller et al. 2015, Cantiello et al. 2016). We further investigate this scenario by considering first the oscillation spectrum of the core of a giant star modeled by a stably stratified, self-gravitating fluid sphere pervaded by a uniform and/or toroidal magnetic field. First results show a great sensitivity of the g-mode spectrum to the strength of the magnetic field. This result leads us to further investigate the possibility of using the observed spectra to determine the dissipative properties of the core and the strength of the magnetic field when modeled by a simple large-scale distribution (i.e. uniform and/or toroidal). Results of these investigations will be presented.