Recently it was conjectured by Gibbons and Townsend that the large n limit of an N=4 superconformal extension of the n-particle Calogero model might provide a microscopic description of the extreme Reissner–Nordström black hole near the horizon. In this paper a possibility to construct an SU(1,1|2) invariant extension of the Calogero model is considered. We treat in detail the two-particle case and comment on some peculiarities intrinsic to n > 2 generalizations.