We assess the potential of using presupernova neutrino signals at the Jiangmen Underground Neutrino Observatory (JUNO) to probe the yet-unknown neutrino mass hierarchy. Using models for stars of 12, 15, 20, and 25M⊙, we find that if the ν¯e signals from such a star can be predicted precisely and the star is within ≈440–880 pc, the number of ν¯e+p→n+e+ events detected within one day of its explosion allows to determine the hierarchy at the ≳95% confidence level. For determination at this level using such signals from Betelgeuse, which is at a distance of ≈222 pc, the uncertainty in the predicted number of signals needs to be ≲14–30%. In view of more realistic uncertainties, we discuss and advocate a model-independent determination using both νe and ν¯e signals from Betelgeuse. This method is feasible if the cosmogenic background for ν-e scattering events can be reduced by a factor of ∼2.5–10 from the current estimate. Such reduction might be achieved by using coincidence of the background events, the exploration of which for JUNO is highly desirable.