We observed the field of EP240919a (Liang et al., GCN 37561), also identified as GRB 240919A (Liang et al., GCN 37564; Rodi et al., GCN 37573; Wang et al., GCN 37574) with the REM 60 cm robotic telescope located at the ESO observatory of La Silla (Chile). The observations were carried in the g, r, i, z, J, H, and K bands, started on 2024 September 19 at 23:27:28 UT (i.e. 8.6 hr after the burst), and lasted for about 1 hour. From preliminary inspection of the images, we do not find any optical/NIR counterpart within the EP error circle down to the following 3sigma limit: r > 20.8 (AB; calibrated against the Pan-STARRS catalogue); H > 17.3 (Vega; calibrated against the 2MASS catalogue); at a mid-time of 9.1 hours after the trigger.