Western Mediterranean Basin (WMB) is among tsunamigenic zones with numerous historical records of tsunami damage and deaths. Most recently, a moderate tsunami on 21 May 2003 offshore Algeria, North Africa, was a fresh call for strengthening tsunami warning capabilities in this enclosed water basin. Here, we propose to deploy offshore bottom pressure gauges (OBPGs) and to adopt the framework of a tsunami data assimilation (TDA) approach for providing timely tsunami forecasts. We demonstrate the potential enhancement of the tsunami warning system through the case study of the 2003 Algeria tsunami. Four scenarios of OBPG arrangements involving 10, 5, 3 and 2 gauges are considered. The offshore gauges are located at distances of 120-300 km from the North African coast. The warning lead times are 20, 30, 48 and 55 min for four points of interest considered in this study: Ibiza, Palma, Sant Antoni and Barcelona, respectively. The forecast accuracies are in the range of 69-85% for the four OBPG scenarios revealing acceptable accuracies for tsunami warnings. We conclude that installation of OBPGs in the WMB can be helpful for providing successful and timely tsunami forecasts. We note that the OBPG scenarios proposed in this study are applicable only for the case of the 2003 Algeria tsunami. Further studies including sensitivity analyses (e.g., number of OBPG stations; earthquake magnitude, strike, epicenter) are required in order to determine OBPG arrangements that could be useful for various earthquake scenarios in the WMB.