The High-Luminosity Large Hadron Collider (HL-LHC) is designed to achieve higher instantaneous luminosities, enabling the exploration of the rarest processes of the Standard Model (SM). The CMS collaboration has published an Expression of Interest to pursue the study of the central exclusive production processes, using near-beam detectors. This report details both the expected performance and the scientific potential of the CMS near-beam proton spectrometer at the HL-LHC.