The precedence effect (PE) refers to the dominance of directional information carried by a direct sound (lead) over the spatial information contained in its multiple reflections (lags) in sound localization. Although the processes underlying the PE have been largely investigated, the extent to which peripheral versus central auditory processes contribute to this perceptual phenomenon has remained unclear. The present study investigated the contribution of peripheral processing to the PE through a comparison of physiological and psychoacoustical data in the same human listeners. The psychoacoustical experiments, comprising a fusion task, an interaural time difference detection task and a lateralization task, demonstrated a time range from 1 to 4.6–5 ms, in which the PE operated (precedence window). Click-evoked otoacoustic emissions (CEOAEs) were recorded in both ears to investigate the lead–lag interactions at the level of the basilar membrane (BM) in the cochlea. The CEOAE-derived peripheral and monaural lag suppression was largest for ICIs of 1–4 ms. Auditory-evoked brainstem responses (ABRs) were used to investigate monaural and binaural lag suppression at the brainstem level. The responses to monaural stimulation reflected the peripheral lag suppression observed in the CEOAE results, while the binaural brainstem responses did not show any substantial contribution of binaural processes to monaural lag suppression. The results demonstrated that the lag suppression occurring at the BM in a time range from 1 to 4 ms, as indicated by the suppression of the lag-CEOAE, was the source of the reduction in the lag-ABRs and a possible peripheral contributor to the PE for click stimuli.