Neutrinos can be produced in several regions within GRB sources. First some models, like the Collapsar model or the neutron star merger model predict ample (~ 1053 ergs) production of low (MeV) neutrinos. However, no existing or planned detector could see those from cosmological distances. Furthermore, this signal will be swamped in rate by the much more frequent SN neutrino signals which would typically appear closer.
However, GRBs could be detectable sources of high energy neutrinos, with energies ranging from 1014eV to 1017 eV. These neutrinos are produced by internal or external shocks of the GRB process itself and hence are independent of the nature of the progenitor.
To understand the process of neutrino emission recall that neutrinos are "best" produced in nature following pions production in proton-photon or proton-proton collisions. The proton-photon process requires that the photon's energy is around the resonance in the proton's energy frame: namely at ~ 200 MeV. The resulting pion decays emitting neutrinos with a typical energy of ~ 50 MeV in the proton's rest frame. If the proton is moving relativistically, with a Lorentz factor p within the laboratory frame the required photon energy in the lab frame is smaller by a factor of p and the resulting neutrino energy is larger by a factor of p. Depending on the surrounding environment very energetic pions may lose some of their energy before decaying producing a "cooling break" in the neutrino spectrum. In this case the resulting neutrinos' energy will be lower than this naive upper limit.
Within GRBs protons are accelerated up to 1020 eV [422, 429]. The relevant Lorentz factors of these protons range from up to 1011 (at the very high energy tail of the protons distribution). Thus we expect neutrinos up to 1019 eV provided that there is a sufficient flux of photons at the relevant energies so that the pions can be produced and there are no energy loses to the pions.
Paczynski and Xu  and Waxman and Bahcall  calculated the flux of VHE neutrinos from internal shocks. They found that a significant flux of ~ 1014 eV neutrinos can be produced by interaction of the accelerated internal shocks protons with the GRB photons. Guetta et al.  estimate that on average each GRB produces a flux of ~ 10-9 GeV/cm2 sec sr corresponding to 0.01 events in a km3 detector. Calculations of specific fluxes from individual bursts (that factor in the observed -rays spectrum) were performed by Guetta et al . Waxman and Bahcall  suggest that protons accelerated at the reverse shock (that arises at the beginning of the afterglow) would interact with the optical - uv flux of the afterglow and produce 1018 eV neutrinos.
Within the Collapsar model Mészáros and Waxman , Razzaque et al.  suggested that as the jet punches the stellar shell it can produce a flux of TeV neutrinos. Within the Supranova model the internal shock protons  or external shocks protons  can also interact with external, pulsar wind bubble, photons producing 1016 eV neutrinos with a comparable detection rate to the one obtained form interaction of the internal shock protons with -rays photons. If the external magnetic field is sufficiently large (as in the pulsar wind bubble) external shocks can also accelerate protons to high energy . In this case the protons can interact with afterglow photons and can produce neutrinos up to 1017 eV .