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We report the quasi-particle scattering spectroscopy on the heavy-fermion superconductor CeCoIn₅ under pressure. In the normal state above the superconducting transition temperature, a dip in differential conductance (dI/dV) is observed below the characteristic temperature of T_g, indicating a pseudogap with energy ∆_g. When subjected to the external pressure, ∆_g and T_g gradually increase, following the trend of the Kondo coherence temperature (T_coh). The Fano-resonance asymmetry in dI/dV, which could be attributed to delocalization of f-electrons, persists even at elevated temperatures much higher than T_coh and collapses on a single line against the reduced temperature (T/T_sat) among different pressures, signifying the onset of Kondo coherence at T_sat. The dependence on pressure of ∆_g is in sharp contrast to that of superconducting gap ∆_sc, but is consistent with T_coh, showing that the pseudogap observed in CeCoIn₅ is less likely involved in the SC pairing process, but is rather related to Kondo hybridization.