Context. Due to the extreme extinction towards the Galactic centre (A_V ∼ 30 mag), its stellar population is mainly studied in the near-infrared (NIR) regime. Therefore, a proper analysis of the NIR extinction curve is necessary to fully characterise the stellar structure and population of the inner part of the galaxy. Aims. We studied the dependence of the extinction index (α_λ) in the NIR on the line of sight, wavelength, and extinction. Methods. We used the GALACTICNUCLEUS imaging survey, a high angular resolution catalogue (0.2″) for the inner part of the Galaxy in JHK_s, and studied the spatial variation in the extinction index. We also applied two independent methods based on red clump stars to compute the extinction index between different bands and its variation with wavelength. Results. We did not detect any significant line-of-sight or extinction variation in α within the studied region in the nuclear stellar disc. The extinction index between JH and HK_s differs by 0.19 ± 0.05. We obtained mean values for the extinction indices α_JH = 2.43 ± 0.03 and α_HKs = 2.23 ± 0.03. The dependence of the extinction index on the wavelength could explain the differences obtained for α_λ in the literature since it was assumed constant for the NIR regime.