Fused Filament Fabrication (FFF) is an Additive Manufacturing (AM) process that builds up a part via layer by layer deposition of polymeric material. The purpose of this study is to implement viscosity and density models for improving the assessment of melt flow behavior inside the nozzle during deposition. Numerical simulations are carried out for different combinations of important process parameters like extrusion velocity Ve, extrusion temperature Te, and filament material (Acrylonitrile Butadiene Styrene (ABS) and Polylactic Acid (PLA)). Cross-Williams–Landel–Ferry (Cross-WLF) viscosity and Pressure–Volume–Temperature (PVT) density models are incorporated to get realistic results. Distribution of printing parameters like pressure, temperature, velocity and viscosity inside the nozzle are observed at steady state and their relationship with the print quality is discussed. Effect of the PVT model on polymer deposition is illustrated by comparing it with deposition considering a constant density. Velocity profiles are obtained for the different cases considered and locations where the flow is fully developed, along the axial distance of the nozzle, are determined and termed as stable zones. A direct correlation between the position of the developed melt flow profile and printing quality is established and the best combination of printing parameters is proposed for ABS and PLA. Extended stable zones are obtained for the polymer melt in the nozzle at Ve = 60 mm/s, Te = 220 °C for ABS and Ve = 30 mm/s and Te = 195 °C for PLA and hence, these can be considered as the optimum values of the printing parameters.