This work is part of the line of research that focuses on the asynchronous regime of the Kuramoto model, which has received less attention than synchronization phenomena. Focusing on the fully disordered Kuramoto model we analyzed the spectral properties of the multiplicative ”network noise” of the system and found an unexpected non monotonic behaviour of its correlation time. To analytically describe this finding we employed Pr¨user’s approach to reduce the dynamics to a self-consistent stochastic single-oscillator problem and study perturbatively the behaviour of the system in the small-disorder regime. We then exploited a scaling argument to obtain a power law for the large-disorder regime.