The centrosome is positioned at the cell center by pushing and pulling forces transmitted by microtubules (MTs). Centrosome decentering is often considered to result from asymmetric, cortical pulling forces exerted in particular by molecular motors on MTs and controlled by external cues affecting the cell cortex locally. Here we used numerical simulations to investigate the possibility that it could equally result from the redistribution of pushing forces due to a reorientation of MTs. We first showed that MT gliding along cell edges and pivoting around the centrosome regulate MT rearrangement and thereby direct the spatial distribution of pushing forces, whereas the number, dynamics, and stiffness of MTs determine the magnitude of these forces. By modulating these parameters, we identified different regimes, involving both pushing and pulling forces, characterized by robust centrosome centering, robust off-centering, or "reactive" positioning. In the last-named conditions, weak asymmetric cues can induce a misbalance of pushing and pulling forces, resulting in an abrupt transition from a centered to an off-centered position. Taken together, these results point to the central role played by the configuration of the MTs on the distribution of pushing forces that position the centrosome. We suggest that asymmetric external cues should not be seen as direct driver of centrosome decentering and cell polarization but instead as inducers of an effective reorganization of the MT network, fostering centrosome motion to the cell periphery.