In order to prepare the analysis of planned elastic-scattering experiments with a low-energy radioactive {sup 6}He beam on an {alpha} target, we determine a theoretical interaction between these nuclei. A double-folding potential is obtained from a realistic {sup 6}He density derived from a microscopic three-cluster model. Special attention is paid to the {sup 6}He-halo description. The resulting potential displays an unusual long tail which might have observable effects on the elastic cross sections. The parity dependence of the optical potential related to the elastic transfer of the halo neutrons is discussed qualitatively. {copyright} {ital 1996 The American Physical Society.}