Optical applications of chalcogenide glasses need a wide transparency window. Promising glass systems include HgI2. Our recent studies of the yHgI2 (1-y)As2X3 glasses, where X = S, Se, have shown for the first time a significant difference in the mercury local coordination. The sulphide glasses are molecular systems with linear HgI2 molecules incorporated within the AsS3/2 glass network. The selenide glasses are polymeric with [HgIt(Ib)2/2]n chains. The trigonal mercury coordination is unusual in mercury iodides. Two different Hg-I NN coordination in the glass suggest molecular or polymeric structure in the S- or Se-based melt and possibly a liquid-liquid transition in pure HgI2 melt similar to the lambda-transition in liquid sulphur. The proposed experiment is aimed to clarify these hypotheses.