Gravitational-wave (GW) and kilonova (KN) measurements have established binary neutron star (BNS) mergers as a significant site for the production of the heaviest elements in our Universe. Under hot and dense conditions such as those encountered in BNS mergers, neutrino transport effects play a crucial role in mass outflows and in shaping the composition of the ejecta. As such, in order to model a BNS merger, neutrino emission, propagation and absorption need to be taken into consideration. Here, we elaborate on a truncated moments scheme evolving the first two moments of the neutrino radiation field, which we are currently implementing in the 3D general relativistic moving-mesh code AREPO. We also discuss the first test results obtained with this scheme for an idealized setup of a homogeneous sphere.