We use the EAGLE simulations to study the oxygen abundance gradients of gas discs in galaxies within the stellar mass range [10^9.5, 10^10.8]Mo at z=0. The estimated median oxygen gradient is -0.011 (0.002) dex kpc^-1, which is shallower than observed. No clear trend between simulated disc oxygen gradient and galaxy stellar mass is found when all galaxies are considered. However, the oxygen gradient shows a clear correlation with gas disc size so that shallower abundance slopes are found for increasing gas disc sizes. Positive oxygen gradients are detected for ~40 per cent of the analysed gas discs, with a slight higher frequency in low mass galaxies. Galaxies that have quiet merger histories show a positive correlation between oxygen gradient and stellar mass, so that more massive galaxies tend to have shallower metallicity gradients. At high stellar mass, there is a larger fraction of rotational-dominated galaxies in low density regions. At low stellar mass, non-merger galaxies show a large variety of oxygen gradients and morphologies. The normalization of the disc oxygen gradients in non-merger galaxies by the effective radius removes the trend with stellar mass. Conversely, galaxies that experienced mergers show a weak relation between oxygen gradient and stellar mass. Additionally, the analysed EAGLE discs show no clear dependence of the oxygen gradients on local environment, in agreement with current observational findings.