This paper investigates the potential role of concentrated solar power (CSP) in off-grid green electrolytic hydrogen and ammonia production using an open-source techno-economic assessment optimization model. The green ammonia plant comprises a flexible Haber-Bosch loop, an electrolyzer park, a desalination plant, storage systems (thermal, electrical, and hydrogen), and a power supply optionally including wind power, solar photovoltaic (PV), and CSP (solar tower or parabolic trough collectors). Various system configurations and cost assumptions are tested to evaluate when CSP technologies are economically viable for green fuel production. Results demonstrate that CSP and thermal energy storage (TES) technologies can play a minor but useful role in providing nighttime power supply to the ammonia plant, in combination with onshore wind power and electrical storage. Solar PV with 1-axis tracking remains the primary power provider, and the optimal system always includes large-scale hydrogen storage. In the cheapest configuration, the LCOA reaches 646 €/tNH3. With an 80% reduction in CSP and TES costs, CSP technology becomes a major player in power production. In scenarios where hydrogen storage is not feasible and the ammonia plant lacks full flexibility, a 20% cost reduction (to 2750 €/kW) is enough for them to become major power providers.