We present our experimental and theoretical study on Co diffusion in the first few atomic layers of Cu(001). While the diffusion of Co atoms in Cu(001) is usually expected to be intense at a temperature T≥800 K, in the vicinity of the surface, it is already activated at a considerably lower temperature T∼650 K whereas the diffusion in the deep bulk region is still inhibited. This intense near-surface diffusion provides an accumulation of Co atoms in the first six atomic layers upon a single stage Co deposition. The details of the near-surface diffusion are studied by analyzing the distribution of the location depth of the buried single Co atoms. The depth of location of single Co atoms is deduced from scanning tunneling microscopy (STM) data. The subsurface Co atoms induce a perturbation of the electron density of states of the surface which is observable as apparent ringlike ripples in the STM images of the atomically flat Cu surface. The depth of location of the buried Co atoms is determined from the diameter of those rings. The largest amount of Co atoms is found to be in the third layer, emphasizing that the near-surface diffusion should be described by diffusion parameters different from those for bulk diffusion. A model that describes the embedding process of Co atoms into Cu(001) layers is developed. The model assumes Co atoms to diffuse via the vacancy and ring-exchange mechanisms. The energy barriers for the interlayer Co diffusion via those mechanisms are calculated using the nudged elastic band method. The model satisfactorily explains the experimental results. Our study reveals that the energy barriers for Co diffusion in the first five atomic layers of Cu(001) are lower than those in the bulk. This defines the region in which Co diffusion should be considered as a near-surface one.