The application of micro/nanotechnologies in the development of food contact materials is currently of great interest for the food technology sector. The materials for this purpose include various types of polymers, among which are PLGA (polylactic-co-glycolic acid) and PCL (polycaprolactone), biodegradable synthetic polymers. Electrospinning is a low-cost and easily reproducible technique for the production of polymeric micro/nanofiber membranes that can be used in the packaging of food. This work establishes the parameters for the manufacturing, by means of electrospinning, of micro/nanofiber membranes made of PLGA, PCL and a combination of both of these polymers. The resulting fibers were characterized via scanning electron microscopy. Given the importance, within the food industry, of knowing the effect that the package components may have on bacterial proliferation, the resulting fibers were incubated with three of the most frequent microorganisms that contaminate food: Staphylococcus aureus, Enterococcus faecalis and Escherichia coli. Both the viability and the bacterial adhesion were quantitatively determined in terms of the biofilm formation capacity. The formation of biofilms was greater in the PLGA membranes. When any of the microorganisms were exposed to the membranes made of the mixture of the two polymers, or with only PCL, a marked reduction in the formation of biofilm was observed. These results show that it is possible, by means of a proper selection of the materials, to reduce the possibility of contamination in both the packaging and the food, without the need to add products that might be inconvenient due to their possible side effects.