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GRB 201015A is a long-duration Gamma-Ray Burst (GRB) which was detected at very high energies (> 100 GeV) using the MAGIC telescopes. If confirmed, this would be the fifth and least luminous GRB ever detected at this energies. We performed a radio follow-up of GRB 201015A over twelve different epochs, from 1.4 to 117 days post-burst, with the Karl G. Jansky Very Large Array, e-MERLIN and the European VLBI Network. We included optical and X-rays observations, performed with the Multiple Mirror Telescope and the Chandra X-ray Observatory respectively, together with publicly available data. We detected a point-like transient, consistent with the position of GRB 201015A until 23 and 47 days post-burst at 1.5 and 5 GHz, respectively. The source was detected also in both optical (1.4 and 2.2 days post-burst) and X-ray (8.4 and 13.6 days post-burst) observations. The multi-wavelength afterglow light curves can be explained with the standard model for a GRB seen on-axis, which expands and decelerates into a medium with a homogeneous density, while a circumburst medium with a wind-like profile is disfavoured. Notwithstanding the high resolution provided by the VLBI, we could not pinpoint any expansion or centroid displacement of the outflow. If the GRB is seen at the viewing angle which maximises the apparent velocity, we estimate that the Lorentz factor for the possible proper motion is $Γ_α$ < 40 in right ascension and $Γ_δ$ < 61 in declination. On the other hand, if the GRB is seen on-axis, the size of the afterglow is <5 pc and <16 pc at 25 and 47 days. Finally, the early peak in the optical light curve suggests the presence of a reverse shock component before 0.01 days from the burst.