Understanding the mechanisms which relate properties of liquid and solid phases is crucial for fabricating new advanced solid materials, such as glasses, quasicrystals and high-entropy alloys. Here we address this issue for quasicrystal-forming Al-Cu-Fe alloys which can serve as a model for studying microscopic mechanisms of quasicrystal formation. We study experimentally two structural-sensitive properties of the liquid -- viscosity and undercoolability -- and compare results with textit{ab initio} investigations of short-range order (SRO). We observe that SRO in Al-Cu-Fe melts is polytetrahedral and mainly presented by distorted Kasper polyhedra. However, topologically perfect icosahedra are almost absent an even stoichiometry of icosahedral quasicrystal phase that suggests the topological structure of local polyhedra does not survive upon melting. It is shown that the main features of interatomic interaction in Al-Cu-Fe system, extracted from radial distribution function and bong-angle distribution function, are the same for both liquid and solid states. In particular, the system demonstrates pronounced repulsion between Fe and Cu as well as strong chemical interaction between Fe and Al, which are almost concentration-independent. We argue that SRO and structural-sensitive properties of a melt may serve as useful indicators of solid phase formation. In particular, in the concentration region corresponding to the composition of the icosahedral phase, a change in the chemical short-range order is observed, which leads to minima on the viscosity and udercoolability isotherms and has a noticeable effect on the initial stage of solidification.
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