Dark matter annihilation signals coming from Galactic subhaloes may account for a small fraction of unassociated point sources detected in the second Fermi-LAT Catalogue (2FGL). To investigate this possibility, we present SIBYL, a Random Forest classifier that offers predictions on class memberships for unassociated Fermi-LAT sources at high Galactic latitudes using gamma-ray features extracted from the 2FGL. SIBYL generates a large ensemble of classification trees that are trained to vote on whether a particular object is an active galactic nucleus (AGN) or a pulsar. After training on a list of 908 identified/associated 2FGL sources, SIBYL reaches individual accuracy rates of up to 97.7 per cent for AGNs and 96.5 per cent for pulsars. Predictions for the 269 unassociated 2FGL sources at |b|>=10{deg} suggest that 216 are potential AGNs and 16 are potential pulsars (with majority votes greater than 70 per cent). The remaining 37 objects are inconclusive, but none is an extreme outlier. These results could guide future quests for dark matter Galactic subhaloes.