Individuals with diverse motor abilities often benefit from intensive and specialized rehabilitation therapies aimed at enhancing their functional recovery. Nevertheless, the challenge lies in the restricted availability of neurorehabilitation professionals, hindering the effective delivery of the necessary level of care. Robotic devices hold great potential in reducing the dependence on medical personnel during therapy but, at the same time, they generally lack the crucial human interaction and motivation that traditional in-person sessions provide. To bridge this gap, we introduce an AI-based system aimed at delivering personalized, out-of-hospital assistance during neurorehabilitation training. This system includes a rehabilitation training device, affective signal classification models, training exercises, and a socially interactive agent as the user interface. With the assistance of a professional, the envisioned system is designed to be tailored to accommodate the unique rehabilitation requirements of an individual patient. Conceptually, after a preliminary setup and instruction phase, the patient is equipped to continue their rehabilitation regimen autonomously in the comfort of their home, facilitated by a socially interactive agent functioning as a virtual coaching assistant. Our approach involves the integration of an interactive socially-aware virtual agent into a neurorehabilitation robotic framework, with the primary objective of recreating the social aspects inherent to in-person rehabilitation sessions. We also conducted a feasibility study to test the framework with healthy patients. The results of our preliminary investigation indicate that participants demonstrated a propensity to adapt to the system. Notably, the presence of the interactive agent during the proposed exercises did not act as a source of distraction; instead, it positively impacted users' engagement.