Extrapolation of the results of some optical model (OM) study of the α-nucleus elastic scattering at incident energies up to 700 MeV implies that the α-nucleus potential becomes repulsive above 910 MeV. To check this assumption, a detailed OM analysis of the elastic α+12C and α+40Ca scattering data at the incident energy of 1370 MeV has been performed using different forms of the optical potential. A realistic pattern of the near-side/far-side interference, required to reproduce the diffractive minima in the measured elastic cross sections, strongly suggests that the corresponding optical potentials are still attractive. The folding model prediction for the α+12C and α+40Ca optical potentials using the impulse approximation has been considered. This approximation, which uses the t-matrix parametrization of free nucleon-nucleon (NN) interaction as the model input, was found to be inadequate to give a good account of the data. Consequently, the medium modifications of the NN interaction remain important at this energy. In addition, similar failure of a density dependent NN interaction (CDM3Y6), which works quite well at lower energies, stresses the need for a more appropriate effective NN interaction in this energy region.