HD 327083 is a luminous B type star which exhibits emission lines and an infrared excess and is therefore classified as a supergiant B[e] star. In addition, the star is the primary of a close binary system. It is not clear whether the B[e] behaviour of HD 327083 is related to its binarity or its evolutionary state. Here we address this issue by studying its circumstellar environment with high spatial resolution. To this end, we have observed HD 327083 with the VLTI and AMBER in the medium resolution K-band setting. (CO)-C-13 bandhead emission is detected, confirming HD 327083 is a post-main sequence object. The observations spatially resolve the source of the NIR continuum and the Br gamma and CO line emission. In addition, differential phase measurements allow us to probe the origin of the observed Br gamma emission with sub-mas precision. Using geometrical models, we find that the visibilities and closure phases suggest that the close binary system is surrounded by a circum-binary disk. We also find that in the case of the binary HD 327083, the relative sizes of the continuum and Br gamma emitting regions are different to those of a single supergiant B[e] star where the standard dual outflow scenario is thought to apply. These findings are consistent with the hypothesis that the mass loss of HD 327083 is related to its binary nature.