In the search for new thermoelectric materials, quasicrystals have been investigated due to their inherently low thermal conductivity. Crystalline phases called approximants which are closely related to the quasicrystals, however, have largely been ignored. These approximants have similar structure, yet the periodicity of a crystal. In this paper, we have investigated an icosahedral i-AlCuFe quasicrystalline phase as well as two of its corresponding approximant phases (ω and β). Electrical and thermal transport properties of these materials are presented. The viability of the i-AlCuFe quasicrystalline system and the ω and β approximant phases as thermoelectric materials is discussed.