We aim at investigating whether the chemical composition of the outer region of the protosolar nebula can be consistent with current estimates of the elemental abundances in the ice giants. To do so, we use a self-consistent evolutionary disc and transport model to investigate the time and radial distributions of H2O, CO, CO2, CH3OH, CH4, N2 and H2S, i.e. the main O-, C-, N and S-bearing volatiles in the outer disc. We show that it is impossible to accrete a mixture composed of gas and solids from the disc with a C/H ratio presenting enrichments comparable to the measurements (approx. 70 times protosolar). We also find that the C/N and C/S ratios measured in Uranus and Neptune are compatible with those acquired by building blocks agglomerat...