To grasp an object, we need to move the arm toward it and assume the appropriate hand configuration. While previous studies suggested dorsomedial and dorsolateral pathways in the brain specialized respectively for the transport and grip components, more recent studies cast doubt on such a clear-cut distinction. It is unclear, however, to which degree neuronal populations selective for the two components overlap, and if so, to which degree they interact. Here, we used multivoxel pattern analysis (MVPA) of functional magnetic resonance imaging (fMRI) data to investigate the representation of three center-out movements (touch, pincer grip, whole-hand grip) performed in five reach directions. We found selectivity exclusively for reach direction in posterior and rostral superior parietal lobes (SPLp, SPLr), supplementary motor area (SMA), and the superior portion of dorsal premotor cortex (PMDs). Instead, we found selectivity for both grip type and reach direction in the inferior portion of dorsal premotor cortex (PMDi), ventral premotor cortex (PMv), anterior intraparietal sulcus (aIPS), primary motor (M1), somatosensory (S1) cortices and the anterior superior parietal lobe (SPLa). Within these regions, PMv, M1, aIPS and SPLa showed weak interactions between the transport and grip components. Our results suggest that human PMDi and S1 contain both grip- and reach-direction selective neuronal populations that retain their functional independence, whereas this information might be combined at the level of PMv, M1, aIPS, and SPLa.