Plasmonic gold nanoparticles are normally used as sensor to detect analytes permanently bound to their surface. If the interaction between the analyte and the nanosensor surface is negligible, it only diffuses through the sensor's sensing volume, causing a small temporal shift of the plasmon resonance position. By using a very sensitive and fast detection scheme, we are able to detect these small fluctuations in the plasmon resonance. With the help of a theoretical model consistent with our detection geometry, we determine the analyte's diffusion coefficient. The method is verified by observing the trends upon changing diffusor size and medium viscosity, and the diffusion coefficients obtained were found to reflect reduced diffusion close to a solid interface. Our method, which we refer to as NanoPCS (for nanoscale plasmon correlation spectroscopy), is of practical importance for any application involving the diffusion of analytes close to nanoparticles.