This paper presents the numerical assessment of a modular steel sleeve connection incorporating a wedge locking mechanism, developed to enhance reusability and sustainability in steel construction. The connection eliminates welding and drilling of the main members, enabling full disassembly and reuse. An adapted configuration was investigated for central column applications, where multiple beams frame into a single square hollow section column through a four-sided sleeve. Finite element models were developed in Abaqus to evaluate the structural response, focusing on stress redistribution, plastic strain development, and moment–rotation behavior. The results indicate that yielding shifts away from the column face toward the sleeve–beam interface, promoting hinge formation in the beam rather than in the joint core. The connection demonstrates semi-rigid behavior consistent with Eurocode classifications, with stiffness comparable to conventional bolted joints. Overall, the study highlights the potential of modular sleeve connections with wedge locking mechanisms as reliable, demountable alternatives to traditional welded or bolted joints, supporting circular economy strategies in steel construction.