Context. There are now strong indications that white dwarf (WD) stars with masses well below the Chandrasekhar limit (M Ch ≈ 1.4 M ) contribute a significant fraction of SN Ia progenitors. The relative fraction of stable iron-group elements synthesized in the explosion has been suggested as a possible discriminant between M Ch and sub-M Ch events. In particular, it is thought that the higherdensity ejecta of M Ch WDs, which favours the synthesis of stable isotopes of nickel, results in prominent [Ni ii] lines in late-time spectra ( 150 d past explosion). Aims. We study the explosive nucleosynthesis of stable nickel in SNe Ia resulting from M Ch and sub-M Ch progenitors, and explore the potential for lines of [Ni ii] in the optical an near-infrared (at 7378 Å and 1.94 µm) in late-time spectra to serve as a diagnostic of the exploding WD mass. Methods. We review stable Ni yields in a large variety of published SN Ia models. Using 1D M Ch delayed-detonation and sub-M Ch detonation models, we study the synthesis of stable Ni isotopes (in particular 58 Ni), and investigate the formation of [Ni ii] lines using nonlocal thermodynamic equilibrium radiative-transfer simulations with the CMFGEN code. Results. We confirm that stable Ni production is in general more efficient in M Ch explosions at solar metallicity (typically 0.02-0.08 M for the 58 Ni isotope), but note that the 58 Ni yields in sub-M Ch events systematically exceed 0.01 M for WDs more massive than one solar mass. We find that the radiative proton-capture reaction 57 Co(p, γ) 58 Ni is the dominant production mode for 58 Ni in both M Ch and sub-M Ch models, while the α-capture reaction on 54 Fe has a negligible impact on the final 58 Ni yield. More importantly, we demonstrate that the lack of [Ni ii] lines in late-time spectra of sub-M Ch events is not always due to an under-abundance of stable Ni, but results from the higher ionization of Ni in the inner ejecta. Conversely, the strong [Ni ii] lines predicted in our 1D M Ch models are completely suppressed when 56 Ni is sufficiently mixed with the innermost layers rich in stable iron-group elements. Conclusions. [Ni ii] lines in late-time SN Ia spectra have a complex dependency on the abundance of stable Ni, which limits their use alone in distinguishing between M Ch and sub-M Ch progenitors. However, we argue that a low-luminosity SN Ia displaying strong [Ni ii] lines would most likely result from a Chandrasekhar-mass progenitor.