The increasing growth in knowledge about the functioning of the nervous system of mammals and humans, as well as the significant neuromorphic technology developments in recent decades, has led to the emergence of a large number of brain–computer interfaces and neuroprosthetics for regenerative medicine tasks. Neurotechnologies have traditionally been developed for therapeutic purposes to help or replace motor, sensory or cognitive abilities damaged by injury or disease. They also have significant potential for memory enhancement. However, there are still no fully developed neurotechnologies and neural interfaces capable of restoring or expanding cognitive functions, in particular memory, in mammals or humans. In this regard, the search for new technologies in the field of the restoration of cognitive functions is an urgent task of modern neurophysiology, neurotechnology and artificial intelligence. The hippocampus is an important brain structure connected to memory and information processing in the brain. The aim of this paper is to propose an approach based on deep neural networks for the prediction of hippocampal signals in the CA1 region based on received biological input in the CA3 region. We compare the results of prediction for two widely used deep architectures: reservoir computing (RC) and long short-term memory (LSTM) networks. The proposed study can be viewed as a first step in the complex task of the development of a neurohybrid chip, which allows one to restore memory functions in the damaged rodent hippocampus.