ABSTRACT We present results from MUSE observations of a 21-cm ${\rm H\, {\small I}}$ absorption system detected with the Australian Square Kilometre Array Pathfinder radio telescope at redshift z = 0.4503 towards the z = 1.71 quasar PKS 1610-771. We identify four galaxies (A, B, X, and Y) at the same redshift as the 21-cm ${\rm H\, {\small I}}$ Damped Lyman-α (DLA) absorption system, with impact parameters ranging from less than 10 kpc to almost 200 kpc from the quasar sightline. ${\rm Ca\, {\small II}}$ and ${\rm Na\, {\small I}}$ absorption is seen in the MUSE spectrum of the background QSO, with velocities coinciding with the initial ${\rm H\, {\small I}}$ 21-cm detection, but tracing less dense and warmer gas. This metal-line component aligns with the rotating ionized disc of galaxy B (impact parameter 18 kpc from the QSO) and appears to be corotating with the galaxy disc. In contrast, the 21-cm ${\rm H\, {\small I}}$ absorber is blueshifted relative to the galaxies nearest the absorber and has the opposite sign to the velocity field of galaxy B. Since galaxies A and B are separated by only 17 kpc on the sky and 70 km s−1 in velocity, it appears likely that the 21-cm detection traces extragalactic clouds of gas formed from their interaction. This system reveals that the cold 100 K neutral gas critical for star formation can be associated with complex structures beyond the galaxy disc, and is a first case study made in preparation for future large 21-cm absorption surveys like the ASKAP First Large Absorption Survey in ${\rm H\, {\small I}}$.