High-entropy alloys (HEA) are a group of modern, perspective materials that have been intensively developed in recent years due to their superior properties and potential applications in many fields. The complexity of their chemical composition and the further interactions of main elements significantly inhibit the prediction of phases that may form during material processing. Thus, at the design stage of HEA fabrication, the molecular orbitals theory was proposed. In this method, the connection of the average strength of covalent bonding between the alloying elements (Bo parameter) and the average energy level of the d-orbital (parameter Md) enables for a preliminary assessment of the phase structure and the type of lattice for individual components in the formed alloy. The designed TiCoCrFeMn alloy was produced by the powder metallurgy method, preceded by mechanical alloying of the initial elementary powders and at the temperature of 1050 °C for 60 s. An ultra-fine-grained structured alloy was homogenized at 1000 °C for 1000 h. The X-ray diffraction and scanning electron microscopy analysis confirmed the correctness of the methodology proposed as the assumed phase structure consisted of the body-centered cubic (BCC) solid solution and the C14 Laves phase was obtained.