Unlike other manufacturing techniques, additive manufacturing enables part consolidation through the production of multi-material parts with enhanced functionality. With reference to the functionality of monitoring the structural integrity of a product during its use, conductive filaments can be used in additive manufacturing. This work aims to investigate the applications of multi-material fused filament fabrication to produce embedded strain gauges for real-time monitoring of part deformations. In layer-by-layer fabrication, conductive filaments can be used to produce strain-sensitive elements inside products at a low cost. This preliminary study demonstrated the feasibility of the proposed approach using tensile samples fabricated through additive manufacturing. The samples were produced using a polyethylene terephthalate glycol filament and an acrylonitrile styrene acrylate filament, while electrically conductive polylactic acid was used for the strain gauge. The characterization and testing activities were conducted by comparing the results of the tensile testing with data acquired through an experimental system set up with an Arduino board, aligning with the resistance-based strain gauge theory. The findings show that the co-fabricated strain gauge successfully traces part deformation, enabling real-time monitoring of strain in the elastic field. Nevertheless, further optimization of the proposed approach is imperative to enhance the reliability and accuracy of the methodology.