Lyman-α nebulae are typically found in massive environments at high redshift (z ≳ 2). The origin of their Lyman-α (Lyα) emission remains debated. Recent polarimetric observations showed that at least some Lyα sources are polarized. This is often interpreted as proof that the photons are centrally produced and contradicts the scenario in which the Lyα emission is the cooling radiation emitted by gas that is heated during the accretion onto the halo. We suggest that this cooling radiation scenario is compatible with the polarimetric observations. To test this idea, we post-processed a radiative hydrodynamics simulation of a blob with the MCLya Monte Carlo transfer code. We computed radial profiles for the surface brightness and the degree of polarization and compared them to existing observations. We found that computed and observed profiles both are consistent with a significant contribution of the extragalactic gas to the Lyα emission. Most of the photons are centrally emitted and are subsequently scattered inside the filament, which produces the observed high level of polarization. We argue that the contribution of the extragalactic gas to the Lyα emission does not prevent polarization. On the contrary, we find that pure galactic emission causes the polarization profile to be too steep to be consistent with observations.