  Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$
have raised intensive debates on its exact gap symmetry, while a satisfactory
theoretical basis is still lacking. Here we propose a phenomenological approach
to calculate the superconducting gap functions, taking into consideration both
the realistic Fermi surface topology and the intra- and interband quantum
critical scatterings. Our calculations yield a nodeless $s^\pm$-wave solution
in the presence of strong interband pairing interaction, in good agreement with
experiments. This provides a possible basis for understanding the
superconducting gap symmetry of CeCu$_2$Si$_2$ at ambient pressure and
indicates the potential importance of multiple Fermi surfaces and interband
pairing interaction in understanding heavy fermion superconductivity.
