  The IceCube Collaboration initially reported the detection of 37
extraterrestrial neutrinos in the TeV - PeV energy range. The reconstructed
neutrino events were obtained during three consecutive years of data taking,
from 2010 to 2013. Although these events have been discussed to have an
extragalactic origin, they have not been correlated to any known source.
Recently, the IceCube Collaboration reported a neutrino-induced muon event with
energy of $2.6\pm0.3$ PeV which corresponds to the highest event ever detected.
Neither the reconstructed direction of this event (J2000.0), detected on June
11 2014 at R.A.=110$^\circ$.34, Dec.=11$^\circ$.48 matches with any familiar
source. Long gamma-ray bursts (lGRBs) are usually associated with the core
collapse of massive stars leading relativistic-collimated jets inside stars
with high-energy neutrino production. These neutrinos have been linked to the
37 events previously detected by IceCube experiment. In this work, we explore
the conditions and values of parameters so that the highest neutrino recently
detected could be generated by proton-photon and proton-hadron interactions at
internal shocks inside lGRB progenitor star and then detected in IceCube
experiment. Considering that internal shocks take place in a relativistic
collimated jet, whose (half) opening angle is $\theta_0\sim$ 0.1, we found that
lGRBs with total luminosity $L\lesssim 10^{48}$ erg/s and internal shocks on
the surface of progenitors such as Wolf-Rayet (WR) and blue super giant (BSG)
stars favor this multi-PeV neutrino production, although this neutrino could be
associated to $L\sim 10^{50.5}$ ($\sim 10^{50}$) erg/s provided that the
internal shocks occur at $\sim 10^9$ ($\sim 10^{10.2}$) cm for a WR (BSG).
