The European Demonstration Fusion Power Reactor (EU-DEMO) has to operate in a completely tritium self-sufficient mode after initial start-up, which includes producing excess tritium to allow the start-up of other reactors. The initial start-up inventory is mainly dictated by operational inventories in the fuel cycle (FC). Advances in FC technologies and immediate recycling of a large fraction of the torus exhaust gas in the direct internal recycling loop are expected to contribute greatly to an overall low operational inventory. The remainder of the torus exhaust gas, as well as tritium from the blankets, nevertheless requires treatment in the tritium plant in order to perform the necessary purification and isotope rebalancing. Here, the employed systems still feature significant operational inventories and predominantly require steady-state operation in order to maximize their performance. In this paper the operational tritium inventories in the major FC systems are reported based on the pre-concept FC design. Additionally, major dependencies of these inventories on key design drivers of the FC are discussed. It is predicted that the EU-DEMO FC will be able to operate with an overall tritium inventory of less than 2 kg.