Production of neutrinos is abundant at LHC. Flavour composition and energy reach of the neutrino flux from proton-proton collisions depend on the pseudorapidity $eta$. At large $eta$, energies can exceed the TeV, with a sizeable contribution of the $tau$ flavour. A dedicated detector could intercept this intense neutrino flux in the forward direction, and measure the interaction cross section on nucleons in the unexplored energy range from a few hundred GeV to a few TeV. The high energies of neutrinos result in a larger $ u$N interaction cross section, and the detector size can be relatively small. Machine backgrounds vary rapidly while moving along and away from the beam line. Four locations were considered as hosts for a neutrino detector: the CMS quadruplet region (~25 m from CMS Interaction Point (IP)), UJ53 and UJ57 (90 and 120 m from CMS IP), RR53 and RR57 (240 m from CMS IP), TI18 (480 m from ATLAS IP). The potential sites are studied on the basis of (a) expectations for neutrino interaction rates, flavour composition and energy spectrum, (b) predicted backgrounds and in-situ measurements, performed with a nuclear emulsion detector and radiation monitors. TI18 emerges as the most favourable location. A small detector in TI18 could measure, for the first time, the high-energy $ u$N cross section, and separately for $tau$ neutrinos, with good precision, already with 300 fb$^{-1}$ in the LHC Run3.
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