The police and the English Football Association have already launched investigations into Clattenburg's alleged use of "inappropriate language" toward the Nigeria international during Chelsea's 3-2 loss to United on Sunday.
On Wednesday, Chelsea sent a file of evidence to the FA, including statements from players and staff members who they claim witnessed Mikel being abused by Clattenburg.
The referee has yet to publicly respond to the allegations after being reported to have used to the word "monkey."
"I don't believe Mark Clattenburg would make any comments like that. I refuse to believe it," Ferguson said. "I think it is unthinkable in the modern climate. I just don't believe it, simple as that. There is no way a referee would stoop to that. I am convinced of that."
Ferguson later claimed on United's TV channel that Clattenburg's "career is teetering on the brink."
"The stigma unattached to it is unfair unless they (Chelsea) have proof he actually said that — which I don't believe," Ferguson said.
Backing Clattenburg further, Ferguson added: "The problem now is ... how Chelsea can get themselves out of this situation because it's pretty serious."
The Scotsman, who has been in charge at United since 1986, said in the last 15 years no player had complained to him about abuse from a referee.
"I think in the modern game, the way we see the game today rather than how it was 25 years ago, it has completely changed," Ferguson said. "I played myself and I know the banter that went on between referees and players 25 years ago is different from today."
Ferguson's defence of Clattenburg comes a day after Arsenal manager Arsene Wenger claimed Chelsea made the allegations "with little proof."
"I'm not a great believer in making these stories public," Wenger said. "I am a deep supporter of doing that internally. If (football) becomes a sport to make the lawyers rich, I am not a fan of it."
Chelsea manager Roberto Di Matteo wouldn't directly respond to the comments made by Ferguson and Wenger.
"We are against any form of discrimination," Di Matteo said. "We will support anybody who is fighting that."
The latest racism saga emerged just as English football seemed to be moving on from the year-long John Terry case. The Chelsea captain is now serving a four-match ban for racially abusing Queens Park Rangers defender Anton Ferdinand during a Premier League match last year.
But the police and Chelsea also opened investigations on Thursday after a fan was pictured making a monkey gesture during the second meeting between Chelsea and United at Stamford Bridge in the League Cup on Wednesday.
Di Matteo said tougher action might need to be taken to eradicate racism, which blighted English football in the 1970s and 80s.
"The fact that these incidents are happening, and (get) a lot of media exposure, maybe makes people aware that we need to fight a problem that we have in society and maybe fight it a little bit stronger than we thought," he said.
The government said it wants the Football Association to address the problem quickly.
"We expect the football authorities to come forward with a clear plan of action in the coming weeks on what more can be done to tackle racism in the game," British sports minister Hugh Robertson said in Friday's editions of the Daily Telegraph newspaper. "Events over the last year have shown the need for action."