The paramagnetic spectral response of the intermediate-valence compound CeNi has been studied by inelastic neutron scattering on isotopically ${(}^{60}\mathrm{Ni})$ enriched single-crystal and powder samples. At low temperature $(T\ensuremath{\sim}10\mathrm{K}),$ no magnetic intensity was found up to an energy $E\ensuremath{\approx}15\mathrm{meV},$ indicating a spin-gap-like response. The absence of detectable quasielastic scattering in high-resolution time-of-flight spectra provides clear evidence for the formation of a singlet ground state due to electron correlations. The magnetic response measured at $T=11\mathrm{K}$ on the single crystal consists of (i) a broad structureless contribution, extending beyond 60 meV, which is a characteristic feature of valence-fluctuating materials, and (ii) two extra narrow peaks at about 18 and 34 meV, which exist for practically all Q vectors investigated, and whose intensities vary as a function of both the reduced q vector and the direction in reciprocal space. This behavior is quite unusual among intermetallic intermediate-valence compounds. It implies that the mixed-valence state in CeNi cannot be described by a single-ion Anderson model, and that magnetic correlations should be taken into account. The extra peaks are tentatively related to crystal-field interactions, which are of the same order of magnitude here as the Kondo temperature.