The theory developed by Scheutjens and Fleer to describe polymer adsorption and depletion is used to calculate the density profile of nonadsorbing polymers near a surface. The theory predicts damped oscillations in the segment density profile with a wavelength of about the coil size. As a consequence, the interaction energy between two surfaces immersed in a solution of nonadsorbing polymers is an oscillatory function of the separation distance, too. The decay length of the oscillations is proportional to the coil size and independent of the polymer concentration. The oscillations are associated with a liquid-like layering of polymer coils near the surface. An increase in concentration or chain length causes a decrease in the amplitude of the oscillations, because the stronger interpenetration of the coils suppresses inhomogeneities. In dilute solutions no oscillations are observed, because the decay length of the oscillations is smaller than the depletion correlation length, in analogy with the Fisher-Widom criterion in simple fluids. For polymer solutions it is found that the Fisher-Widom condition coincides with the overlap concentration. Our results show that the blob size is not the only relevant length scale above the overlap concentration. The size of the individual coils plays a role, too.