In the last years, experimental/theoretical studies have shown that graphene has a strong affinity toward nucleobases, serving as a promising nanomaterial for self-assembly, sensing, and/or sequencing of DNA/RNA constituents. Then, a complete picture of the properties of the nucleobase-graphene systems is required for its use in technological applications. This work describes a detailed quantum chemical analysis of the aromaticity of adsorbed nucleobases on graphene, comparing between aromaticity indexes based on magnetic, geometry, electron density, and electron delocalization properties of graphene-nucleobase systems. Contrary to the stated by magnetic-based aromaticity criteria (such as nucleus-independent chemical shifts), it is proved that the aromatic character of nucleobases is not increased/decreased upon binding on graphene. Therefore, magnetic aromaticity criteria are not recommended to analyze aromaticity in related systems, unless a fragmented scheme be adopted. Finally, these results are expected to expand the knowledge about the understanding of biomolecules-graphene interactions.