The crystal structure of Cu+Re7+O4 is capable of a quasi-reversible incorporation of C3H7OH molecules. A room-temperature reaction between CuReO4 and C3H7OH under oxidizing conditions leads to the formation of a novel metal-organic hybrid compound Cu2+(C3H7OH)2(ReO4)2. Upon heating under reducing conditions, this compound transforms back into CuReO4, albeit with ReO2 and metallic Cu as by-products. The crystal structure of Cu(C3H7OH)2(ReO4)2 solved from single-crystal X-ray diffraction (Pbca, a=10.005(3)Å, b=7.833(2)Å, and c=19.180(5)Å) reveals layers of corner-sharing CuO6-octahedra and ReO4-tetrahedra, whereas isopropyl groups are attached to both sides of these layers, thus providing additional connections within the layers through hydrogen bonds. Cu(C3H7OH)2(ReO4)2 is paramagnetic down to 4K because the spatial arrangement of the Cu2+ half-filled orbitals prevents magnetic superexchange. The paramagnetic effective moment of 2.0(1) μB is slightly above the spin-only value and typical for Cu2+ ions.