The VEGAS imaging survey of the Hydra I cluster has revealed an extended network of stellar filaments to the south-west of the spiral galaxy NGC 3314A. Within these filaments, at a projected distance of ∼ 40 kpc from the galaxy, we discover an ultra-diffuse galaxy (UDG) with a central surface brightness of µ 0,g ∼ 26 mag arcsec −2 and effective radius R e ∼ 3.8 kpc. This UDG, named UDG 32, is one of the faintest and most diffuse low-surface-brightness galaxies in the Hydra I cluster. Based on the available data, we cannot exclude that this object is just seen in projection on top of the stellar filaments and is thus instead a foreground or background UDG in the cluster. However, the clear spatial coincidence of UDG 32 with the stellar filaments of NGC 3314A suggests that it might have formed from the material in the filaments, becoming a detached, gravitationally bound system. In this scenario, the origin of UDG 32 depends on the nature of the stellar filaments in NGC 3314A, which is still unknown. The stellar filaments could result from ram-pressure stripping or have a tidal origin. In this letter we focus on the comparison of the observed properties of the stellar filaments and of UDG 32 and speculate on their possible origin. The relatively red colour (g − r = 0.54 ± 0.14 mag) of the UDG, similar to that of the disk in NGC 3314A, combined with an age older than 1 Gyr and the possible presence of a few compact stellar systems, points towards a tidal formation scenario.