The 27-year-old could even consider his future at Old Trafford, one insider claimed, adding: "The incident was obviously an accident but Becks was absolutely furious, as you would be if you had just got a boot in the face."
Beckham, who had been substituted during Saturday's 2-0 defeat, drove away from the ground with a dressing on his face 25 minutes before the other players, accompanied by his wife Victoria, 28, and three-year-old son Brooklyn.
There is no suggestion that 61-year-old Sir Alex meant to hurt Beckham, who was taken off after injuring his right leg in the second half of the fifth-round tie. But the bust-up shocked not only Beckham and his family but all the players and staff.
Jimmy Greaves, football commentator and former England player, said: "If anyone thought Fergie was calming down after turning 60, they are very wrong. He will need to make up with the player before the situation starts to overshadow their season."
Sir Alex has acquired a fearsome reputation for his dressing-room rages. Former United striker Mark Hughes described the manager's "hairdryer" treatment: "He would stand nose-to-nose with you and just shout and bawl, and you would end up with your hair behind your head."
Mark McGhee, the Millwall manager who was a player under Ferguson at Aberdeen, described another incident at the Scottish club when Sir Alex burst into the dressing room as a reserve team were changing following a poor performance.
McGhee said: "There was a pile of dirty kit in the middle of the room and he just kicked it all up in the air. A pair of underpants shot across the room and landed on this young player's head. He was so scared as Alex then launched into the lad next to him that he just didn't move. It was only when Alex finally turned to him and shouted, 'What the hell have you got those on your head for?' that he took them off."
Today a Manchester United spokesman refused to comment on Saturday's incident, saying: " Whatever happens in the dressing room remains private." SFX Sports Group, which represents Beckham, also declined to comment, passing calls on to the club.
* Victoria Beckham is set to host a "summit" dinner in which all five original Spice Girls will meet for the first time in five years. Industry sources believe top of the agenda is a much-delayed greatest hits album which could lead to a promotional tour.