  The $\pi_0$ neutral meson pole mass is calculated in a strongly magnetized
medium using the SU(2) Nambu-Jona-Lasinio model within the random phase
approximation (RPA) at zero temperature and zero baryonic density. We employ a
magnetic field dependent coupling, $G(eB)$, fitted to reproduce lattice QCD
results for the quark condensates. Divergent quantities are handled with a
magnetic field independent regularization scheme in order to avoid unphysical
oscillations. A comparison between the running and the fixed couplings reveals
that the former produces results much closer to the predictions from recent
lattice calculations. In particular, we find that the $\pi_0$ meson mass
systematically decreases when the magnetic field increases while the scalar
mass remains almost constant. We also investigate how the magnetic background
influences other mesonic properties such as $f_{{\pi}_0}$ and $g_{\pi_0 q q}$.
