The interaction between graphene and germanium surfaces was investigated using a combination of microscopic and macroscopic experimental techniques and complementary theoretical calculations. Density functional theory (DFT) calculations for different reconstructions of the Ge(001) surface showed that the interactions between graphene and the Ge(001) surface introduce additional peaks in the density of states, superimposed on the graphene valence and conduction energy bands. The growth of graphene induces nanofaceting of the Ge(001) surface, which exhibits well-organized hill and valley structures. The graphene regions covered by hills are of high quality and exhibit an almost linear dispersion relation, which indicates weak graphene-germanium interactions. On the other hand, the graphene component occupying valley regions is significantly perturbed by the interaction with germanium. It was also found that the stronger graphene-germanium interaction observed in the valley regions is connected with a lower local electrical conductivity. Annealing of graphene/Ge(001)/Si(001) was performed to obtain a more uniform surface. This process results in a surface characterized by negligible hill and valley structures; however, the graphene properties unexpectedly deteriorated with increasing uniformity of the Ge(001) surface. To sum up, it was shown that the mechanism responsible for the formation of local conductivity inhomogeneities in graphene covering the Ge(001) surface is related to the different strength of graphene-germanium interactions. The present results indicate that, in order to obtain high-quality graphene, the experimental efforts should focus on limiting the interactions between germanium and graphene, which can be achieved by adjusting the growth conditions.