The effect of a mean fluid velocity gradient on the particle-fluid velocity covariance and fluctuating relative velocity for a small solid particle suspended in a turbulent gas is examined using Fourier transform techniques. The presence of such a gradient is shown to elevate the covariance above the level predicted without it. The variance of the fluctuating relative velocity is not directly affected by the presence of a mean velocity gradient. The possible impact on turbulence modulation by particles is discussed.