The energetic feedback that is generated by radio jets in active galactic nuclei (AGNs) has been suggested to be able to produce fast outflows of atomic hydrogen (HI) gas that can be studied in absorption at high spatial resolution. We have used the Very Large Array (VLA) and a global very-long-baseline-interferometry (VLBI) array to locate and study in detail the HI outflow discovered with the Westerbork Synthesis Radio Telescope (WSRT) in the re-started radio galaxy 3C 236. We confirm, from the VLA data, the presence of a blue-shifted wing of the HI with a width of $sim1000mathrm{,km,s^{-1}}$. This HI outflow is partially recovered by the VLBI observation. In particular, we detect four clouds with masses of $0.28text{-}1.5times 10^4M_odot$ with VLBI that do not follow the regular rotation of most of the HI. Three of these clouds are located, in projection, against the nuclear region on scales of $lesssim 40mathrm{,pc}$, while the fourth is co-spatial to the south-east lobe at a projected distance of $sim270mathrm{,pc}$. Their velocities are between $150$ and $640mathrm{,km,s^{-1}}$ blue-shifted with respect to the velocity of the disk-related HI. These findings suggest that the outflow is at least partly formed by clouds, as predicted by some numerical simulations and originates already in the inner (few tens of pc) region of the radio galaxy. Our results indicate that all of the outflow could consist of many clouds with perhaps comparable properties as the ones detected, distributed also at larger radii from the nucleus where the lower brightness of the lobe does not allow us to detect them. However, we cannot rule out the presence of a diffuse component of the outflow. The fact that 3C 236 is a low excitation radio galaxy, makes it less likely that the optical AGN is able to produce strong radiative winds leaving the radio jet as the main driver for the HI outflow.