Among the registered extremely high energy cosmic rays (EHECR, E=3.2·1020 eV) an event with the highest to date energy of E=3.2·1020 eV was detected by the Fly"s Eye experiment (FE event) in 1991. With the use of the back-tracking method for the calculation of the EHECR trajectories in Galactic and extragalactic magnetic fields, we show that the galaxies UGC 03574 and UGC 03394 are the most promising candidates among the nearby extragalactic sources for the cases of iron and C-N-O group primary nucleusrespectively. The most likely accelerating mechanisms are the newly-born millisecond pulsars, magnetar flares and tidal disruption events in these galaxies.
