The blown extrusion of poly(lactic acid) presents several challenges mainly due to its poor elongation properties. This work deals on the possibility to enhance the processabiliy of PLA by film blowing by functionalizing the polymer with nanosilicates. In particular, two types of polylactic acid (PLA 4032D and PLA 4042D) and different types of filler, selected from montmorillonites (Cloisite 30B) and bentonites (Nanofil SE3010) families, were used to prepare the hybrid systems by using a twin-screw extruder. The interaction between the polymer and the clay was evaluated by FTIR analysis and correlated to the structure of the obtained nanocomposites in terms of clay dispersion. All the samples were then submitted to rheological measurements both in shear and elongational mode. The addition of C30B to the PLA4032D resin appears the more suitable solution to improve the processability of PLA by film blowing extrusion. In fact, the C30B nanoparticles, being well dispersed and having good adhesion with the PLA 4032D matrix, cause a significant increment in the drawability of the neat polymer and they also enhance the extensional viscosity of the poly(lactic acid) at low elongation rates, with positive effects on the bubble stability.