In this work we investigate the role of electronic correlations on the electron-impact induced onization spectrum of free fullerene clusters. The unperturbed valence states of the clusters are described within the Hartree-Fock scheme based on a jellium shell model. To account for the many-body response of the cluster to an external perturbation we utilize the random phase approximation with exchange in order to describe the interaction of the incoming projectile with the metallic cluster which introduced the effect of non-local screening of the inter-electronic interaction. Within this framework we evaluate numerically the ionization transition amplitudes and compare the results with available experimental data for a C₆₀ cluster. We point out that the neglect of the collective response of the cluster leads to results at variance with experimental finding.