XMMSL1 J171900.4–353217 is a very-faint X-ray transient that was discovered in 2010 March when it exhibited an outburst. We report on 7 observations, obtained with the X-Ray Telescope (XRT) aboard the Neil Gehrels Swift Observatory between 2010 May and October. By fitting a single absorbed power-law model to the XRT spectra, we infer power-law indices of Γ = 1.8 &minus 2.7 and an absorption column density of NH = (4.6‑7.9)×1022 cm‑2. The inferred 0.5‑10 keV luminosity fluctuated irregularly and peaked at LX ≃ 1035 ‑ 1036 erg s‑1 for a distance of 4 ‑ 12 kpc. Based on the evolution of the power-law index with varying luminosity, we propose that the source most likely is a transient neutron star low-mass X-ray binary located at several kpc. If true, it would be a good candidate to search for coherent millisecond pulsations when it enters a new accretion outburst.