This paper presents a model that describes a possible mechanism for electromagnetic (EM) signal transmission and reception by bacterial cells within their biofilm communities. Bacterial cells in biofilms are embedded into a complex extracellular matrix containing, among other components, charged helical nanofibrils from amyloid-forming peptides. Based on the current knowledge about the nanoscale structure and dynamics of the amyloids, we explore a hypothetical model that the mechanical vibration of these nanofibrils allows the cells to transmit EM signals to their neighboring cells and the surrounding environment. For the reception, the induced electric field can either exert force on the charges of adjacent nanofibrils associated with the neighboring cells or affect the placement/conformation of a certain charged messenger protein within the cell. The proposed model is based on a coupled system of electrical and mechanical nanoscale structures, which predicts signal transmission and reception within kHz-GHz frequency ranges. Different mechanisms for generating EM signals at various frequency bands related to the structure of the cell and their biofilm constituents are discussed.