Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a non-equilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much larger than the equilibrium one for small enough wave number. In the case of diffusion in binary mixtures such fluctuations are time-symmetric, notwithstanding the fact that they are generated by a non-equilibrium condition. In this paper, we investigate diffusion of two solutes in a ternary liquid mixture by means of fluctuating hydrodynamics theory. We show that the time cross-correlation function of the concentrations is not time-symmetric, hence showing that time-symmetry is violated for such non-equilibrium fluctuations. We discuss the feasibility of experiments aimed at the detection of the asymmetry of the cross correlation function of non-equilibrium concentration fluctuations in ternary mixtures, as envisaged in the Giant Fluctuations (NEUF-DIX) microgravity project of the European Space Agency.