The High Energy cosmic-Radiation Detection (HERD) facility has been proposed as one of the main experiments on board the Chinese space station. HERD is scheduled to be installed around 2027 and to operate for at least 10 years. Its main scientific goals are the study of the cosmic ray spectrum and composition up to the PeV energy range, indirect dark matter detection, and all-sky gamma-ray observation above 100 MeV. HERD features a novel design in order to optimize its acceptance per weight, with a central 3D imaging calorimeter surrounded on top and on its four lateral sides by complementary subdetectors. A dedicated trigger, dubbed the ultra-low-energy gamma-ray (ULEG) trigger, is required to enable the detection of gamma rays down to ~100 MeV. The ULEG trigger design is based upon the search for energy deposition patterns on the tracker and the anticoincidence shield, compatible with the conversion of a gamma ray within the tracker volume and resulting in enough tracker hits to allow for a good-quality gamma-ray direction reconstruction. We describe the current status of the design of the ULEG trigger system. We also characterize its performance in detecting gamma rays as inferred from Monte Carlo studies.