Abstract: The Five-hundred-meter Aperture Spherical Radio Telescope (FAST) Core Array is a proposed extension of FAST, integrating 24 secondary 40-m antennas implanted within 5 km of the FAST site. This original array design will combine the unprecedented sensitivity of FAST with a high angular resolution (4.3" at a frequency of 1.4 GHz), thereby exceeding the capabilities at similar frequencies of next-generation arrays such as the Square Kilometre Array Phase 1 or the next-generation Very Large Array. This article presents the technical specifications of the FAST Core Array, evaluates its potential relatively to existing radio telescope arrays, and describes its expected scientific prospects. The proposed array will be equipped with technologically advanced backend devices, such as real-time signal processing systems. A phased array feed receiver will be mounted on FAST to improve the survey efficiency of the FAST Core Array, whose broad frequency coverage and large field of view（FOV） will be essential to study transient cosmic phenomena such as fast radio bursts and gravitational wave events, to conduct surveys and resolve structures in neutral hydrogen galaxies, to monitor or detect pulsars, and to investigate exoplanetary systems. Finally, the FAST Core Array can strengthen China's major role in the global radio astronomy community, owing to a wide range of potential scientific applications from cosmology to exoplanet science.