Temporal envelope modulations (TEMs) are one of the most important features that cochlear implant (CI) users rely on to understand speech. Electroencephalographic assessment of TEM encoding could help clinicians to predict speech recognition more objectively, even in patients unable to provide active feedback. The acoustic change complex (ACC) and the auditory steady-state response (ASSR) evoked by low-frequency amplitude-modulated pulse trains can be used to assess TEM encoding with electrical stimulation of individual CI electrodes. In this study, we focused on amplitude modulation detection (AMD) and amplitude modulation frequency discrimination (AMFD) with stimulation of a basal versus an apical electrode. In twelve adult CI users, we (a) assessed behavioral AMFD thresholds and (b) recorded cortical auditory evoked potentials (CAEPs), AMD-ACC, AMFD-ACC, and ASSR in a combined 3-stimulus paradigm. We found that the electrophysiological responses were significantly higher for apical than for basal stimulation. Peak amplitudes of AMFD-ACC were small and (therefore) did not correlate with speech-in-noise recognition. We found significant correlations between speech-in-noise recognition and (a) behavioral AMFD thresholds and (b) AMD-ACC peak amplitudes. AMD and AMFD hold potential to develop a clinically applicable tool for assessing TEM encoding to predict speech recognition in CI users.