Objective. This study aims to design and implement the first Deep Learning (DL) model to classify subjects in the prodromic states of Alzheimer’s Disease (AD) based on resting-state electroencephalographic signals. Approach. EEG recordings of 17 Healthy Controls (HC), 56 Subjective Cognitive Decline (SCD) and 45 Mild Cognitive Impairment (MCI) subjects were acquired at resting state. After preprocessing, we selected sections corresponding to eyes-closed condition. Five different datasets were created by extracting Delta, Theta, Alpha, Beta and Delta-to-Theta frequency bands using bandpass filters. To classify SCD vs MCI and HC vs SCD vs MCI, we propose a framework based on the Transformer architecture, which uses Multi-Head Attention to focus on the most relevant parts of the input signals. We trained and validated the model on each dataset with a leave-one-subject-out cross-validation approach, splitting the signals into 10-second epochs. Subjects were assigned to the same class as the majority of their epochs. Classification performances of the Transformer were assessed for both epochs and subjects and compared with other DL models. Main results. Results showed that the Delta dataset allowed our model to achieve the best performances for the discrimination of SCD and MCI, reaching an AUC of 0.807, while the highest results for the HC vs SCD vs MCI classification were obtained on Alpha and Theta with a micro-AUC higher than 0.74. Significance. We demonstrated that DL approaches can support the adoption of non-invasive and economic techniques as EEG to stratify patients in the clinical population at risk for AD. This result was achieved since the attention mechanism was able to learn temporal dependencies of the signal, focusing on the most discriminative patterns, achieving state-of-the-art results by using a deep model of reduced complexity. Our results were consistent with clinical evidence that changes in brain activity are progressive when considering early stages of AD.