The production of electroconductive nanofiber membranes made from polylactic acid (PLA) coated with polypyrrole (PPy) is investigated, performing a scanning of different reaction parameters and studying their physicochemical and dielectric properties. Depending on PPy content, a transition between conduction mechanisms is observed, with a temperature‐dependent relaxation process for samples without PPy, a temperature‐independent conduction process for samples with high contents of PPy and a combination of both processes for samples with low contents of PPy. A homogeneous and continuous coating is achieved from 23 wt% PPy, observing a percolation effect around 27 wt% PPy. Higher wt% PPy allow to obtain higher conductivities, but PPy aggregates appear from 34% wt% PPy. The high conductivity values obtained for electrospun membranes both through‐plane and in‐plane (above 0.05 and 0.20 S cm–1, respectively, at room temperature) for the highest wt% of PPy, their porous structure with high specific surface area and their thermal stability below 140 °C make them candidates for many potential applications as solid polymer electrolytes in, for example, batteries, supercapacitors, sensors, photosensors, or polymer electrolyte membrane fuel cells (PEMFCs). In addition, the biocompatibility of PLA‐PPy membranes expand their potential applications also in the field of tissue engineering and implantable devices.