Among the sample of Galactic transient X-ray binaries (SXTs) discovered to date, about 70 have been proposed as likely candidates to host a black hole. Yet, only 19 have been dynamically confirmed. Such a reliable confirmation requires phase-resolved spectroscopy of their companion stars, which is generally feasible when the system is in a quiescent state. However, since most of the SXT population lies in the galactic plane, which is strongly affected by interstellar extinction, their optical brightness during quiescence usually falls beyond the capabilities of the current instrumentation (R ≳ 22). To overcome these limitations and thereby increase the number of confirmed Galactic black holes, a correlation between the full-width at half maximum (FWHM) of the Hα line and the semi-amplitude of the donor's radial velocity curve (K2) was presented in the past. Here, we extend the FWHM-K2 correlation to the near-infrared (NIR), exploiting disc lines such as He Iλ10830, Paγ, and Brγ, in a sample of dynamically confirmed black-hole SXTs. We obtain K2 = 0.22(3) FWHM, in good agreement with the optical correlation derived using Hα. The similarity of the two correlations seems to imply that the widths of Hα and the NIR lines are consistent in quiescence. When combined with information on orbital periods, the NIR correlation allows us to constrain the mass of the compact object of systems in quiescence by using single-epoch spectroscopy. We anticipate that this new correlation will give access to highly reddened black hole SXTs, which cannot be otherwise studied at optical wavelengths.