The Tyrrhenian Sea plays an important role in the winter deep water formation in the northwestern Mediterranean through the water that enters the Ligurian Sea via the Corsica Channel. Therefore, the study of the impact of the changes on the future climate on the Tyrrhenian circulation and its consequences represents an important issue. Furthermore, the seasonally dependent Tyrrhenian circulation, which is rich in dynamical mesoscale structures, is dominated by the interplay of local climate and the basin-wide Mediterranean circulation via the water transport across its major straits, and an adequate representation of its features represents an important modeling challenge. In this work we examine with a regionally coupled atmosphere-ocean model the changes in the Tyrrhenian circulation by the end of the 21st century under the RCP8.5 emission scenario, their driving mechanisms, and their possible impact on winter convection in the NW Mediterranean. Our model successfully reproduces the main features of the Mediterranean Sea and Tyrrhenian Basin present-day circulation. We find that toward the end of the century the winter cyclonic along-slope stream around the Tyrrhenian Basin becomes weaker. This weakening increases the wind work transferred to the mesoscale structures, which become more intense than at present in winter and summer. We also find that, in the future, the northward water transport across the Corsica Channel towards the Liguro-Provençal basin becomes smaller than today. Also, water that flows through this channel presents a stronger stratification because of a generalized warming with a freshening of upper and a saltening of intermediate waters. Both factors may contribute to the interruption of deep water formation in the Gulf of Lions by the end of the century.