We present a search for ANTARES neutrino events in spatial and temporal coincidence with IceCube High-Energy Starting Events (HESE). This analysis uses a maximum likelihood ratio approach based on track events due to muons induced by neutrino interactions observed with ANTARES. Each HESE is treated as the signature of a potential transient neutrino source while the neutrino burst duration, the source direction and the number of ANTARES signal events are obtained as those maximising the likelihood. Before applying the method to the unblinded ANTARES dataset, its sensitivity and discovery potential are computed through dedicated pseudo-experiments. This study provides an effective way to acquire information on the possible origin of the IceCube astrophysical signal from transient sources.