Context. Transient neutrino sources such as gamma-ray bursts (GRBs) and supernovae (SNe) are hypothesized to emit bursts of high-energy neutrinos on a time-scale of less than or similar to 100 s. While GRB neutrinos would be produced in high relativistic jets, core-collapse SNe might host soft-relativistic jets, which become stalled in the outer layers of the progenitor star leading to an efficient production of high-energy neutrinos.