We use microfocus Brillouin light scattering spectroscopy to study the interaction of spin current with magnetic fluctuations in a Permalloy microdisk located on top of a Pt strip carrying an electric current. We show that the fluctuations can be efficiently suppressed or enhanced by different directions of the electric current. Additionally, we find that the effect of spin current on magnetic fluctuations is strongly influenced by nonlinear magnon-magnon interactions. The observed phenomena can be used for controllable reduction of thermal noise in spintronic nanodevices.