Context. While Euclid is an ESA mission specifically designed to investigate the nature of dark energy and dark matter, the planned unprecedented combination of survey area (similar to 15000 deg(2)), spatial resolution, low sky-background, and depth also make Euclid an excellent space observatory for the study of the low surface brightness Universe. Scientific exploitation of the extended low surface brightness structures requires dedicated calibration procedures that are yet to be tested.Aims. We investigate the capabilities of Euclid to detect extended low surface brightness structure by identifying and quantifying sky-background sources and stray-light contamination. We test the feasibility of generating sky flat-fields to reduce large-s...