The emergence of magnetic reconstructions at the interfaces of oxide heterostructures are often explained via subtle modifications in the electronic densities, exchange couplings, or strain. Here an additional possible route for induced magnetism is studied in the context of the (LaNiO$_3$)$_n$/(LaMnO$_3$)$_n$ superlattices using a hybrid tight-binding model. In the LaNiO$_3$ region, the induced magnetizations decouple from the intensity of charge leakage from Mn to Ni, but originate from the spin-filtered quantum confinement present in these nanostructures. In general, the induced magnetization is the largest for the (111)-stacking and the weakest for the (001)-stacking superlattices, results compatible with the exchange bias effects reported by Gibert et al. Nat. Mater. 11, 195 (2012).