The iron abundance relative to alpha-elements in the circumnuclear region of quasars is regarded as a clock of the star formation history and, more specifically, of the enrichment by Type Ia supernovae. We investigate the iron abundance in a sample of 22 quasars in the redshift range 3.0 < z < 6.4 by measuring their rest-frame UV Fe II bump, which is shifted into the near-IR, and by comparing it with the Mg II lambda2798 flux. The observations were performed with a device that can obtain near-IR spectra in the range 0.8 - 2.4 mum in one shot, thereby enabling an optimal removal of the continuum underlying the Fe II bump. We detect iron in all quasars including the highest redshift (z = 6.4) quasar currently known. The uniform observational technique and the wide redshift range allow a reliable study of the trend of the Fe II/ Mg II ratio with redshift. We find that the Fe II/ Mg II ratio is nearly constant at all redshifts, although there is marginal evidence for a higher Fe II/ Mg II ratio in the quasars at z similar to 6. If the Fe II/ Mg II ratio reflects the Fe/alpha abundance, this result suggests that the z similar to 6 quasars have already undergone a major episode of iron enrichment. We discuss the possible implications of this finding for the star formation history at z > 6. We also detect a population of weak iron emitters at z similar to 4.5, which are possibly hosted in systems that evolved more slowly. Alternatively, the trend of the Fe II/ Mg II ratio at high redshift may reflect significantly different physical conditions of the circumnuclear gas in such high-redshift quasars.