Several studies are on-going at CERN in the framework of the Physics Beyond Collider study group, with main aim of broadening the physics research spectrum using the available accelerator complex and infrastructure. The possibility to design a layout that allows fixed-target experiments in the primary vacuum of the CERN Large Hadron Collider (LHC), without the need of a dedicated extraction line, is part of these studies. The principle of the layouts presented in this paper is to deflect beam halo protons on a fixed-target placed in the LHC primary vacuum, by means of the channeling process in bent crystals. Moreover, the presence of a second bent crystal adjacent to the target opens a unique opportunity for the first direct measurement of electric and magnetic dipole moments of short-lived baryons. Two possible layouts are reported, together with a thorough evaluation on their expected performance and impact on LHC operations.