Chelsea have made an official complaint to the Football Association over the incident, while the Metropolitan Police have stated that they are working with both parties after also receiving a complaint regarding the referee.
But Sir Alex says that he does not believe a referee would "stoop" to making racist or offensive remarks, and says that he has never had a player make a complaint to him about a referee swearing.
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The Scot told reporters: "I don't believe Mark Clattenburg would make comments like that. I refuse to believe it. I think it's unthinkable in the modern climate. I just don't believe it. It's as simple as that.
"There's no way a referee would stoop to that [racist or offensive remarks]. I'm convinced about that. I think the modern game - if we see the game of 25 years ago - has completely changed. I played myself, and I know the banter goes on between referees and players is completely different from today.
"I've never had a player come to me in the last 15 years and say a referee has sworn at him in a game. Ever. So, that's where I stand. I don't believe it."
The United manager also commented on Saturday's game against Arsenal at Old Trafford, stating that he had no new injury problems, but warning that a repeat of last year's 8-2 victory would not happen again.
He added: "It won't happen again, that's for sure, but it could be a motivation for Arsenal."
The game will come too soon for Chris Smalling, however. The defender is back training with the first-team, with Sir Alex saying that he is not ready yet, but adding that his recovery is encouraging.