The Daily Mail says the incident happened in November 2007 after a match in which Berkovic's son Lior, then nine, was substituted early in the game by Maccabi Herzliya coach Danny Etzioni.
In front of dozens of other parents, former Israel star Berkovic, 36, screamed at Etzioni: "I'll screw you, I'll see you are finished. I'll come after you for the rest of your career."
Immediately after the incident Berkovic said: "Etzioni humiliated my son so I humiliated Etzioni."
Berkovic, who also played for Southampton, Celtic, Blackburn, and Portsmouth until his retirement two years ago, was sentenced to serve 100 hours' community work and ordered to pay Etzioni £400 compensation.