Neutrinos emitted in the carbon, nitrogen, oxygen (CNO) fusion cycle in the Sun are a sub-dominant, yet crucial component of solar neutrinos whose flux has not been measured yet. The Borexino experiment at the Laboratori Nazionali del Gran Sasso (Italy) has a unique opportunity to detect them directly thanks to the detectors radiopurity and the precise understanding of the detector backgrounds. We discuss the sensitivity of Borexino to CNO neutrinos, which is based on the strategies we adopted to constrain the rates of the two most relevant background sources, pep neutrinos from the solar pp-chain and Bi-210 beta decays originating in the intrinsic contamination of the liquid scintillator with Pb-210. Assuming the CNO flux predicted by the high-metallicity Standard Solar Model and an exposure of 1000 daysx71.3 t, Borexino has a median sensitivity to CNO neutrino higher than 3 sigma. With the same hypothesis the expected experimental uncertainty on the CNO neutrino flux is 23%, provided the uncertainty on the independent estimate of the Bi-210 interaction rate is 1.5 cpd/100t. Finally, we evaluated the expected uncertainty of the C and N abundances and the expected discrimination significance between the high and low metallicity Standard Solar Models (HZ and LZ) with future more precise measurement of the CNO solar neutrino flux.