The classical dumbbell and Rouse models for dilute polymer solutions are here modified by introducing an anisotropic diffusivity which mimics the effect of topological interactions arising in polymeric solutions in the vicinity of the overlap concentration c*. Closed-form constitutive equations are derived by making use of typical pre-averaging approximations. Predictions in steady and transient shear flows for tangential and normal stresses are compared to data recently obtained by Osaki et al. (J. Polym. Sci.: Polym. Phys. 38 (2000) 1917), on a polystyrene solution close to c*. As regards the second normal stress difference, more rarely measured, we compare the model predictions with data by Magda et al. (Macromolecules 26 (1993) 1696).