There has been a growing interest in disordered optical media in recent years due to their potential applications in solar collectors, random lasers, light confinement, and other advanced photonic functions. This paper studies the transport of light for different incidence angles in a strongly disordered optical medium composed of core-shell TiO2@Silica nanoparticles suspended in an ethanol solution. A decrease of optical conductance and an increase of absorption near the input border are reported when the incidence angle increases. The specular reflection, measured for the photons that enter the sample, is lower than the effective internal reflection undergone by the coherently backscattered photons in the exact opposite direction, indicating a nonreciprocal propagation of light. This study represents a novel approach in order to understand the complex physics involved at the phase transition to localization.