In the past years, the IceCube Collaboration has reported in several analyses the observation of astrophysical high-energy neutrino events. Despite a compelling evidence for the first identification of a neutrino source, TXS 0506+056, the origin of the majority of these events is still unknown. In this paper, a possible transient origin of the IceCube astrophysical events is searched for using neutrino events detected by the ANTARES telescope. The arrival time and direction of 6894 track-like and 160 shower-like events detected over 2346 days of livetime are examined to search for coincidences with 54 IceCube high-energy track-like neutrino events, by means of a maximum likelihood method. No significant correlation is observed and upper limits on the one-flavour neutrino fluence from the direction of the IceCube candidates are derived. The non-observation of time and space correlation within the time window of 0.1 days with the two most energetic IceCube events constrains the spectral index of a possible point-like transient neutrino source, to be harder than -2.3 and -2.4 for each event, respectively.