Asymmetric cell division generates cell fate diversity during development and adult life. Recent findings have demonstrated that during stem cell divisions, the movement of centrosomes is asymmetric in prophase and that such asymmetry participates in mitotic spindle orientation and cell polarization. Here, we have investigated the dynamics of centrosomes during Drosophila sensory organ precursor asymmetric divisions and find that centrosome movements are asymmetric during cytokinesis. We demonstrate that centrosome movements are controlled by the cell fate determinant Numb, which does not act via its classical effectors, Sanpodo and α-Adaptin, but via the Collapsin Response Mediator Protein (CRMP). Furthermore, we find that CRMP is necessary for efficient Notch signalling and that it regulates the duration of the pericentriolar accumulation of Rab11-positive endosomes, through which the Notch ligand, Delta is recycled. Our work characterizes an additional mode of asymmetric centrosome movement during asymmetric divisions and suggests a model whereby the asymmetry in centrosome movements participates in differential Notch activation to regulate cell fate specification.