A new subsurface growth mode in the Co-Cu system is reported. This mode provides a direct subsurface growth of Co nanoclusters by depositing Co atoms on the Cu(001) surface in a single stage. The resulting subsurface Co nanoclusters are located 2 monolayers (ML) deep below the atomically flat surface of Cu(001). Although these hidden nanoclusters cannot be directly accessed by a scanning tunneling microscopy/spectroscopy (STM/STS) probe, their shape could be deduced using STM/STS via a careful analysis of the local deformation of the Cu(001) surface as well as local variations of surface electron density induced by the subsurface clusters. A strongly asymmetric shape of the nanoclusters is deduced: they are typically 5-10 nm in lateral size but only 2 to 3 ML in thickness. The thickness of the nanoclusters does not evolve significantly under a heat treatment. A simple model is implemented to describe the growth kinetics. The results in this study reveal that intense processes of diffusion, nucleation, and growth take place in a region 1 nm deep, thus defining the near-surface region.