Additive Manufacturing (AM) of polymer composites has enabled the fabrication of highly customized parts with notably mechanical properties, thermal and electrical conductivity compared to un-reinforced polymers. Employing the reinforcements was a key factor in improving the properties of polymers after being 3D printed. However, almost all the existing 3D printing methods could make the most of disparate fiber reinforcement techniques, the fused filament fabrication (FFF) method is reviewed in this study to better understand its flexibility to employ for the proposed novel method. Carbon nanotubes (CNTs) as a desirable reinforcement have a great potential to improve the mechanical, thermal, and electrical properties of 3D printed polymers. Several functionalization approaches for the preparation of CNT reinforced composites are discussed in this study. However, due to the non-uniform distribution and direction of reinforcements, the properties of the resulted specimen do not change as theoretically expected. Based on the phase inversion method, this paper proposes a novel technique to produce CNT-reinforced filaments to simultaneously increase the mechanical, thermal, and electrical properties. A homogeneous CNT dispersion in a dilute polymer solution is first obtained by sonication techniques. Then, the CNT/polymer filaments with the desired CNT content can be obtained by extracting the polymer’s solvent. Furthermore, optimizing the filament draw ratio can result in a reasonable CNT orientation along the filament stretching direction.