Aims. We report the discovery and characterisation of a Lyman α (Lyα) blob close to a galaxy at redshift z = 3.49. We present the analysis we performed to check whether the companion galaxy could be the source of the ionised photons responsible for the Lyα emission from the blob. Methods. We used images obtained from the 10.4 m Gran Telescopio Canarias (GTC) telescope that are part of the Survey of High-z Absorption Red and Dead Sources (SHARDS) project. The blob is only visible in the F551W17 filter, centred around the Lyα line at the redshift of the galaxy. We measured the luminosity of the blob with a two-step procedure. Here, we start with a description of the radial surface-brightness (SB) profile of the galaxy, using a Sérsic function. We then removed this model from the SB profile of the blob and measured the luminosity of the blob alone. We also estimated the Lyα continuum of the galaxy using an Advanced Camera for Surveys (ACS) image from the Hubble Space Telescope (HST) in the F606W filter, which is wider than the SHARDS one and centred at about the same wavelength. In this image, the galaxy is visible, but the blob is not detected, since its Lyα emission is diluted in the larger wavelength range of the F606W filter. Results. We find that the Lyα luminosity of the blob is 1.0 × 1043 erg s‑1, in agreement with other Lyα blobs reported in the literature. The luminosity of the galaxy in the same filter is 2.9 × 1042 erg s‑1. The luminosity within the HST/ACS image that we used to estimate the Lyα continuum emission is Lcont = 1.1 × 1043 erg s‑1. With these values, we have been able to estimate the Lyα equivalent width (EW), found to be 111 Å (rest-frame). This value is in good agreement with the literature and suggests that a super-cluster of massive (1 ‑ 2 × 107 M⊙) and young (2 ‑ 4 Myr) stars could be responsible for the ionisation of the blob. We also used two other methods to estimate the luminosity of the galaxy and the blob to assess the robustness of our results. We find a reasonable agreement that supports our conclusions. It is worth noting that the Lyα blob is spatially decoupled from the galaxy by 3 GTC/SHARDS pixels, corresponding to 5.7 kpc at the redshift of the objects. This misalignment could suggest the presence of an ionised cone of material escaping from the galaxy, as found in nearby galaxies such as M 82.