Hydrogen-fired gas turbines have the potential to play an important role in future -neutral energy and industry sectors. A prerequisite for the operation of hydrogen-fired gas turbines is the availability of sufficient quantities of hydrogen. The combination of electrolysis and renewable power generation is currently considered the most relevant pathway for the large-scale production of -neutral hydrogen. Regarding the fuel supply of hydrogen-fired gas turbines, this pathway is associated with various technical and economic challenges. This applies in particular to configurations in which electrolyzers and hydrogen storage capacities are installed directly at gas turbine sites to avoid hydrogen transport. Considering an exemplary system configuration, this study extends prior model-based investigations by focusing on the economic viability of the on-site fuel supply of hydrogen-fired gas turbines. The impact of various design parameters and operational strategies is analyzed using the levelized cost of hydrogen as the main economic indicator. The study reveals that the investigated on-site hydrogen production is not economically viable within the current (2019) framework of the German energy sector. Assuming the extensive availability of renewable power generation in the long-term, additional investigations indicate that on-site hydrogen production and storage systems for gas turbines could potentially become economically viable if various advantageous conditions are met. These conditions include a sufficient availability of inexpensive renewable power for the operation of electrolyzers as well as a sufficient utilization of on-site hydrogen storage capacities to justify corresponding capital expenditures.