Recent X-ray scattering measurements show that icosahedral short-range order in Ti–Zr–Ni alloys is responsible for a change in phase selection from the stable C14 Laves phase to the quasicrystalline icosahedral phase, and that icosahedral short-range order increases at deeper undercoolings. This change in short-range order should be reflected in changes in the thermophysical properties of the melt. The surface tension and viscosity of quasicrystal-forming Ti–Zr–Ni alloys were measured over a range of temperature, including both stable and undercooled liquids, by an electrostatic levitation (ESL) technique. ESL is a containerless technique which allows processing of samples without contact, greatly reducing contamination and increasing access to the metastable undercooled liquid. The measured viscosity is typical of glass-forming alloys of similar composition to the quasicrystal-forming alloys studied here; however, the surface tension shows an anomaly at deep undercoolings.