We have reported the impact of the core and shell radii on the energy spectrum of centered shallow donor confined inside CdSe/ZnTe core/shell quantum dot and ZnTe/CdSe inverted core/shell quantum dot. The dielectric discontinuity between the nanosystems and their surrounding medium was considered. In order to examine the behavior of the donor binding energy as a function of the spatial parameters a variational approach within the framework of the effective-mass approximation was deployed. Our model shows that for a fixed shell radius the increase of the core radius value blue-shifts the binding energy of the donor inside inverted core/shell quantum dot only if the value of the core to shell radii ratio is between 0.9 and 1, otherwise it is red-shifted. By contrast, for core/shell quantum dot system the binding energy is red-shifted by increasing the core radius for a fixed nanostructure size and for all values of the core to shell radii ratio. We have also found that the donor binding energy values are more important in a core/shell nanodot than in an inverted core/shell quantum dot.