Transport of solutes through membrane channels produces additional noise in the channel ion current because the number of solute molecules in the channel fluctuates. We obtain a general expression for the power spectral density of these fluctuations in a cylindrical channel in the presence of a binding site of arbitrary strength. The expression shows how the spectral density transforms from that in the case of no-binding to the Lorentzian spectral density corresponding to the strong-binding limit. Brownian dynamics simulations confirm our analytical results.