We report on the magnetic excitation spectrum in the normal state of the heavy-fermion superconductor CeCu92)Si(2) on approaching the quantum critical point (QCP). The magnetic response in the superconducting state is characterized by a transfer of spectral weight to energies above a spin excitation gap. In the normal state, a slowing-down of the quasielastic magnetic response is observed, which conforms to the scaling expected for a QCP of spin-density-wave type. This interpretation is substantiated by an analysis of specific heat data and the momentum dependence of the magnetic excitation spectrum. Our study represents the first direct observation of an almost critical slowing-down of the normal state magnetic response at a QCP when suppressing superconductivity. The results strongly imply that the coupling of Cooper pairs in CeCu(2)Si(2) is mediated by overdamped spin fluctuations.