High pressure affects the solidification of glass-forming melts based on aluminum with transition and rare earth metals, allowing the synthesis of new metastable compounds that are stable for quite a long time under normal conditions. An attempt was made to connect high pressure with the glass-forming ability of melts. Using X-ray diffraction and electron microscopy methods, the effect of high pressure (up to 10 GPa) on the solidification of melts of complex multicomponent glass-forming alloys Al86Ni4Co4Gd6, Al86Ni2Co6Gd6, Al86Ni6Go4Gd2Er2, Al86Ni6Co4Gd2Tb2 with a temperature of 1800 K under conditions of rapid cooling was studied. The resulting samples are dense and homogeneous, with a fine-crystalline structure. Under high pressure conditions of 7-10 GPa, metastable crystalline phases were synthesized in alloys. Within the framework of the Ab-Initio Molecular Dynamics approach using density functional theory, the local structure of melts of selected alloys at low and high pressures was studied. The study of short-range order shows the presence of icosahedral clusters in melts, the formation of which is facilitated by rare earth metals. An increase in pressure from 0 to 10 GPa leads to an 8-fold increase in the concentration of icosahedra, resulting in the formation of a "percolation" cluster. It has been shown that the glass-forming ability of melts increases with increasing pressure, which affects the solidification processes. The arrangement of atoms in icosahedral clusters in melts promotes the formation of synthesized metastable crystalline phases in alloys.