We report on the results of a comprehensive observing campaign to reveal the host galaxy of the short GRB 100628A. This burst was followed by a faint X-ray afterglow but no optical counterpart was discovered. However, inside the X-ray error circle a potential host galaxy at a redshift of z = 0.102 was soon reported in the literature. If this system is the host, then GRB 100628A was the cosmologically most nearby unambiguous short burst with a measured redshift so far. We used the multi-colour imager GROND at the ESO/La Silla MPG 2.2 m telescope, ESO/VLT spectroscopy, and deep Australia Telescope Compact Array (ATCA) radio-continuum observations together with publicly available Gemini imaging data to study the putative host and the galaxies in the field of GRB 100628A. We confirm that inside the X-ray error circle the most probable host-galaxy candidate is the morphologically disturbed, interacting galaxy system at z = 0.102. The interacting galaxies are connected by a several kpc long tidal stream, which our VLT/FORS2 spectroscopy reveals strong emission lines of [O ii], [O iii], Hα and Hβ, characteristic for the class of extreme emission-line galaxies and indicative of ongoing star formation. The latter leaves open the possibility that the GRB progenitor was a member of a young stellar population. However, we indentify a second host-galaxy candidate slightly outside the X-ray error circle. It is a radio-bright, luminous elliptical galaxy at a redshift z = 0.311. With a K-band luminosity of 2 × 1011L⊙ this galaxy resembles the probable giant elliptical host of the first well-localized short burst, GRB 050509B. If this is the host, then the progenitor of GRB 100628A was a member of an old stellar population.