We consider and compare the structural properties of bulk TIP4P water and of a sodium chloride aqueous solution in TIP4P water with concentration c = 0.67 mol/kg, in the metastable supercooled region. In a previous paper [D. Corradini, M. Rovere and P. Gallo, J. Chem. Phys. 132, 134508 (2010)] we found in both systems the presence of a liquid-liquid critical point (LLCP). The LLCP is believed to be the end point of the coexistence line between a high density liquid (HDL) and a low density liquid (LDL) phase of water. In the present paper we study the different features of water-water structure in HDL and LDL both in bulk water and in the solution. We find that the ions are able to modify the bulk LDL structure, rendering water-water structure more similar to the bulk HDL case. By the study of the hydration structure in HDL and LDL, a possible mechanism for the modification of the bulk LDL structure in the solution is identified in the substitution of the oxygen by the chloride ion in oxygen coordination shells.