The ERC granted ENUBET project aims at developing the technologies to reduce by a factor $\sim$10 the systematics in neutrino fluxes from conventional beams, allowing measuring the $\nu_e$ (and $\overline{\nu}_e$) cross section with a 1% precision, in the region of interest for future oscillation experiments looking for CP violation. This goal is accomplished by monitoring in an instrumented decay tunnel the high angle positron produced in K$_{e3}$ decays of charged kaons, in a sign and momentum selected narrow band beam. After a brief description of the proposed facility, the Monte Carlo simulation of the positron tagger in realistic conditions and a preliminary event reconstruction chain will be described, together with results on the expected signal selection efficiency.