Coherent elastic neutrino-nucleus scattering (CEvNS) provides a new method to probe the standard model of particle physics at very low energies. The NUCLEUS experiment, situated at the Very-Near-Site (VNS) at the Chooz nuclear power plant, aims to detect antineutrinos emitted from a commercial nuclear reactor via CEvNS at unprecedentetly low recoil energies. For this, the experiment deploys a cryogenic detector system consisting of CaWO4 and Al2O3 target crystals with a total mass of 10g and an ultra low recoil energy threshold of 20 eV. The experimental site provides a high neutrino flux of 1.7x1012 s -1 cm-2 , but being located at shallow ground also offers challenging background conditions. This contribution will give an overview over the plans and status of the individual components which are being developed in order to meet these challenges. These include the passive shielding as well as the active outer and inner veto and the passive vibration decoupling system. Additionally, details on the transition edge sensor based detector system and the expected event rates will be presented.