The Fermilab Mu2e experiment seeks to measure the rare process of direct muon to electron conversion in the field of a nucleus. The magnet system for this experiment is made of three warm-bore solenoids: the Production Solenoid (PS), the Transport Solenoid (TS), and the Detector Solenoid (DS). The TS is an "S-shaped" solenoid set between the other bigger solenoids. The Transport Solenoid has a warm-bore aperture of 0.5 m and field between 2.5 and 2.0 T. The PS and DS have respectively warm-bore aperture of 1.5 m and 1.9 m, and peak field of 4.6 T and 2 T.In order to meet the field specifications the TS starts inside the PS and ends inside the DS. The strong coupling with the adjacent solenoids poses several challenges to the design and operation of the Transport Solenoid. The coil layout has to compensate for the fringe field of the adjacent solenoids. The quench protection system should handle all possible quench and failure scenarios in all three solenoids. The support system has to be able to withstand very different forces depending on the powering status of the adjacent solenoids.In this paper the conceptual design of the Transport Solenoid is presented and discussed focusing on these coupling issues and the proposed solutions.