We investigate the enrichment patterns of several delivery scenarios of the volatiles to the atmospheres of ice giants, having in mind that the only well constrained determination made remotely, namely the carbon abundance measurement, suggests that their envelopes possess highly supersolar metallicities, i.e., close to two orders of magnitude above that of the protosolar nebula. In the framework of the core accretion model, only the delivery of volatiles in solid forms (amorphous ice, clathrates, pure condensates) to these planets can account for the apparent supersolar metallicity of their envelopes. In contrast, because of the inward drift of icy particles through various snowlines, all mechanisms invoking the delivery of volatiles in vapor forms predict subsolar abundances in the envelopes of Uranus and Neptune. Alternatively, even if the disk instability mechanism remains questionable in our solar system, it might be consistent with the supersolar metallicities observed in Uranus and Neptune, assuming the two planets suffered subsequent erosion of their H-He envelopes. The enrichment patterns derived for each delivery scenario considered should be useful to interpret future in situ measurements by atmospheric entry probes.