We studied the noncovalent interactions of gadolinium bisphthalocyanine (GdPc2) with cluster models for graphene and hexagonal boron nitride (hBN) of variable size by using the PBE functional of the generalized gradient approximation in conjunction with Grimme’s dispersion correction and a DND double numerical basis set (that is, PBE-D2/DND). We found that in terms of the bonding strength, changes in the Gd-N bond lengths, the charge and spin of the Gd central ion, and the spin of the GdPc2 molecule, the behaviors of the graphene- and hBN-based model systems are rather similar. As expected, when increasing the size of the graphene and hBN cluster models, the strength of the interaction with GdPc2 increases, in which the bonding with the hBN models is usually stronger by a few kcal/mol. One of the main questions addressed in the present work was whether a change in the antiferromagnetic spin alignment to a ferromagnetic one, which is typical for GdPc2, is (at least theoretically) possible, as it has been observed previously for a number of graphene models when a smaller basis set DN was employed. We found that the use of a larger DND basis set dramatically reduces the occurrence of ferromagnetic adsorption complexes but does not exclude this possibility completely.