Various chemical elements including nickel (Ni) exhibit mass-independent isotope heterogeneity on a bulk meteorite level, which is generally accepted to reflect the heterogeneous distribution of presolar carrier(s) from different nucleosynthetic sources. Thus, understanding the nature of the carriers can help decipher the origin of the observed nucleosynthetic variability, which remains elusive. In this study, we present the first high precision measurements of mass-independent and mass-dependent Ni isotope compositions for step-leaches of the CI chondrite Ivuna and Efremovka CAIs supplemented by bulk chondrite measurements. Step-leaches record highly anomalous Ni isotope signatures that can be attributed to at least four diverse nucleosynthetic sources. The most anomalous leachates show either large deficits (up to 0.1 %) in the neutron-poor 58Ni and 60Ni nuclides (L11, thought to contain mainly s-process derived Ni) or minor enrichments and deficits (∼100 ppm) in 60Ni or 64Ni (L6, L8, L9 and L10, all thought to derive mainly from supernovae). Pristine CAIs record Ni isotope compositions typified by enrichments in 58Ni of up to 400 ppm. Our new data for bulk chondrites agree with earlier work and emphasize the appropriateness of using the 62Ni/61Ni ratio for internal normalization. Based on the compositional relations between the step-leaches data, CAIs, and bulk meteorites, we show that 60Ni variability is consistent with being of nucleosynthetic origin as opposed to reflecting variable Fe/Ni ratios in the presence of live 60Fe. Finally, we infer that the observed Ni nucleosynthetic disk variability is predominantly driven by a combination of processes separating different nucleosynthetic carriers in the disk from each other, including thermal processing and size-based sorting.