Eutectic High-Entropy Alloys (EHEAs) show promise in balancing strength and ductility, along with excellent castability and chemical homogeneity. However, identifying optimal eutectic compositions in HEAs has been a persistent challenge, primarily due to the lacuna of multi-component phase diagrams. In addressing this challenge, the eutectic compositional space in Al-Cr-Fe-Ni is unveiled for the first time as a case study using the High-Throughput Calphad methodology. By integrating the Python application programming interface into Thermo-Calc, Latin Hypercube Sampling generated 100,000 compositions examined for eutectic formation based on thermodynamic parameters. This analysis revealed the significant correlation of valence electron concentration, enthalpy of mixing, and atomic size difference on eutectic formation. Moreover, the predictions of the proposed design methodology were compared with reported eutectic compositions, exhibiting excellent agreement. Further, a novel dual-phase eutectic alloy featuring an FCC+B2 combination predicted through the proposed design framework has been successfully cast, providing further experimental validation.