The aim of this paper is to address a problem raised originally by L. Gendre, later by W. Pleśniak and recently by L. Białas-Cież and M. Kosek. This problem concerns the pluricomplex Green function and consists in finding new examples of sets with so-called Łojasiewicz-Siciak ((ŁS) for short) property. So far, the known examples of such sets are rather of particular nature. We prove that each compact subset of R N , treated as a subset of C N , satisfies the Łojasiewicz-Siciak condition. We also give a sufficient geometric criterion for a semialgebraic set in R 2 , but treated as a subset of C, to satisfy this condition. This criterion applies more generally to a set in C definable in a polynomially bounded o-minimal structure.