In this preliminary work, we consider the problem of detecting cyber-attacks in a linear system equipped with a Model Predictive Controller, where the feedback loop is closed over a non-ideal network, and the process is subject to a random Gaussian disturbance. We adopt a model-based approach in order to detect anomalies, formalizing the problem as a binary hypothesis test. The proposed approach exploits the analytical redundancy obtained by computing partially overlapping nominal system trajectories over a temporal sliding window, and propagating the disturbance distributions along them. The recorded data over such window is then used to define a probabilistic consistency index at each time step in order to make a decision about the presence of possible attacks. Preliminary simulation results show the effectiveness of the proposed attack-detection method.