Bone is a complex structural composite that features a remarkable combination of mechanical properties, in spite of its rather meager building blocks (i.e., mineral and proteins). The reasons behind these optimal mechanical performances lay in bone hierarchical organization. A crucial role is played by the microscale structure (Haversian), which is formed by a repetition of cylindrical building blocks (osteons) surrounded by a matrix of interstitial tissue. Following a biomimetic approach, mimicking this natural architecture in the design of innovative fiber-reinforced composites appears to be a very promising way to improve the performance of engineering composites. However, it is still an open challenge due to manufacturing-induced limitations. Here we aim to overcome such limitations and implement a bone-like design into novel fiber-reinforced materials. We first focus on the design and manufacturing of osteon-like features by pull-winding technology, to get a continuous and rapid production. We fabricate osteon-inspired multilayer concentric rods by coupling multiple layers of fibers, characterized by different materials and orientations. To study the effect of each layer on the overall mechanical properties and provide guidelines for optimal design, we perform finite element simulations. The simplicity and versality of the production line allow us to manufacture great quantities of these rods at a high production rate. The combination of finite elements analysis and experimental design allow us to find a trade-off between the best and the most feasible configuration. Future works will focus on the manufacturing of a multiscale composite laminate made of these small pull-winded rods, inspired by the osteons.