Rhenium (Re) is used as an alloying element in Ni based superalloys but promotes the formation of fragile intermetallic compounds in many systems. The thermodynamic databases that allow the modeling of the properties of Ni based alloys are still incomplete and further data has to be integrated. In this context, we propose a new characterization of the system Mn-Re for temperatures below 1150 degrees C. We evidenced the existence of sigma and chi (alpha Mn) Frank-Kasper phases with very large solubility domains. We took a peculiar attention to the atom distribution in both phases and structural analyses (Rietveld refinement) reveal that Re has a strong preference for atomic sites with high CN. In addition, sigma phase molar enthalpy of formation was measured by drop calorimetry at 1150 degrees C (40 and 55 at.% Re).