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The impact of COVID-19 and the pressure it exerts on health systems worldwide motivated this study, which focuses on the case of Greece. We aim to assist decision makers as well as health professionals, by estimating the short to medium term needs in Intensive Care Unit (ICU) beds. We analyse time series of confirmed cases, hospitalised patients, ICU bed occupancy, recovered patients and deaths. We employ state-of-the-art forecasting algorithms, such as ARTXP, ARIMA, SARIMAX, and Multivariate Regression models. We combine these into three forecasting models culminating to a tri-model approach in time series analysis and compare them. The results of this study show that the combination of ARIMA with SARIMAX is more accurate for the majority of the investigated regions in short term 1-week ahead predictions, while Multivariate Regression outperforms the other two models for 2-weeks ahead predictions. Finally, for the medium term 3-weeks ahead predictions the Multivariate Regression and ARIMA with SARIMAX show the best results. We report on Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), R-squared (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula>), and Mean Absolute Error (MAE) values, for one-week, two-week and three-week ahead predictions for ICU bed requirements. Such timely insights offer new capabilities for efficient management of healthcare resources.