  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.
