Eye witnesses saw Ten Cate aggressively face up to skipper Terry during Saturday's session.
The pair went head to head, hurling a tirade of swear words and insults as players dived in to separate them.
A witness told The Sun: "The session was supposed to put the finishing touches to the final plans for Wembley - but it just descended into a massive row.
"All the players have become exasperated by the shambolic nature of some of the recent training sessions.
"And there was a lot of unrest among the squad because no one knew what the team was going to be for Wembley.
"Everyone was trying to guess what was going on and in the end the frustration became too much. But the intensity of the row took everyone by surprise.
"John and Ten Cate were right in each other's faces and when it became clear that neither was going to back down, other players jumped between them to pull them apart.
"To make matters worse, Mr Abramovich was visiting the training ground and saw the whole thing."
