High-entropy alloys (HEA) are the subject of interest for many scientific researchers, more than 200 thousand publications are currently known on the HEA topic, and their number is growing every day. Particular interest in HEA is caused by the features of their formation and structure, as well as the properties that such alloys possess. Predicting the formation of the structure of high entropy alloys is an important task that will allow obtaining information about new systems without resorting to a complex and expensive experiment. At the moment, there are 2 basic approaches to forecasting the possible phase composition of HEA in the world. The first involves the use of phenomenological parameters based on the Hume-Rothery criteria and thermodynamic quantities, the second—thermodynamic modeling. In the present work, the probability for the existence of the AlNbTiVZr_x system (x = 0.25, 0.5, 1, 1.25) as a high entropy alloy will be considered from a theoretical point of view. HEA are singled out in a special group, since the processes of structure and phase formation in them, as well as the diffusion mobility of atoms, the mechanism of the formation of mechanical properties, and thermal stability differ significantly from similar processes in traditional alloys. The main feature of HEA is the formation of a single-phase thermodynamically stable and high-strength solid substitution solution mainly with an fcc or bcc lattice. In this work, the prediction of a possible phase composition is considered on the example of alloys of the following compositions AlNbTiVZr_0.25, AlNbTiVZr_0.5, AlNbTiVZr, AlNbTiVZr_1.25. The calculations of the phenomenological parameters are performed, the boundary conditions that determine the stability and type of phases are identified. Binary phase diagrams were constructed using the CALPHAD method, which shows the formation of single-phase structures that can be formed in the AlNbTiVZr alloy under study. According to the results of studies, it was found that most likely AlNbTiVZr-based alloys are disordered single-phase solid solutions with a bcc type structure.