In this paper, we begin to explore the use of modern State Space Models (SSMs) for use in Brain Computer Interfaces (BCIs), to predict transcripts of attempted speech from brain recordings in paralyzed patients. Concretely, we replace the Recurrent Neural Network (RNN) in a recent state-of-the-art BCI system with Mamba and S4D. Evaluating our results using phoneme and word error rates, we find that SSMs perform equally or better than an RNN with a similar number of parameters. For computational reasons, we were not able to compare SSMs with as many parameters as the original RNN. Our results may also suggest that SSMs are able correctly generalize and compensate for the natural drift happening on neural data sampled across different days, avoiding the need of using extra preprocessing steps needed with the RNN.