The location of gamma-ray creation and emission within extra-galactic jets is a matter of active debate. One particularly well-suited source to pinpoint the location is the nearby, bright radio galaxy 3C 84, harbouring a powerful jet. Here we investigate the origin of gamma-rays measured during a recent gamma-ray flare, by analysing the linear polarisation signal of close-in-time very long baseline interferometry (VLBI) observations at centimetre and millimetre wavelengths. While 3C 84 is overall almost unpolarised, we find that close-in-time to the gamma-ray flare peak regions at parsec-scale distances from the central engine shows a fractional linear polarisation increase. Under the physically well-motivated assumption of a causal relation between this polarisation enhancement and the gamma-ray flare, and combined with insights from concurrent X-ray polarisation measurements, the gamma-rays being created in this region is a physically motivated scenario, in a process consistent with synchrotron self-Compton.