  The origin of the high-energy flux of neutrinos detected by IceCube is still
unknown. Recent works report the evidence for a possible positional correlation
between the reconstructed neutrino arrival directions and the positions in the
sky of low power, high-energy emitting BL Lac objects (HBL). Assuming that
$\gamma$-ray emitting HBL form the bulk of the sources of high-energy neutrinos
above 100 TeV, we intend to calculate the number of events expected to be
detected for each source by IceCube and KM3NeT. Based on a simple
theoretically-motivated framework inspired by the structured jet scenario for
these sources, we postulate a direct proportionality between high-energy
$\gamma$-ray and neutrino fluxes. We calculate the expected neutrino event rate
for the HBL sources of the Second Fermi-LAT Catalog of High-Energy Sources
(2FHL) for IceCube and the presently under construction KM3NeT using
declination-dependent and exposure-weighted effective areas. We provide a list
of 2FHL HBL with the calculated number of events. For IceCube, the derived
count rate for several sources is relatively high, of the order of $\lesssim$1
yr$^{-1}$, consistently with the recent findings of a possible positional
correlation. For KM3NeT the calculated rates are higher, with several sources
with expected rate exceeding 1 yr$^{-1}$. This, coupled with the improved
angular resolution, implies that the HBL origin can be effectively tested with
few years of observation of KM3NeT (and IceCube Gen2, for which similar
performances are foreseen) through the direct association of neutrinos and
single HBL. Our results show that if -- as hinted by recent works -- HBL
represent a possible population of high-energy neutrino emitters, several
single sources should be identified in few years of exposure of KM3NeT,
highlighting the importance of the improved angular resolution anticipated for
KM3NeT and IceCube Gen2.
