The 37-year-old has been accused of using "inappropriate language" in two incidents allegedly involving John Obi Mikel and Juan Mata during Chelsea's controversial 3-2 defeat to Manchester United at Stamford Bridge on Sunday.
"I would be staggered if he was a racist. In my experience, definitely not," Courtney told BBC Sport.
"We have got to apply zero tolerance to any racism but I would be very, very surprised, shocked, dismayed and disappointed if it was true.
"I've known Mark for many years. He has travelled all over the world, he's refereed players from different backgrounds, cultures, creeds, colours and religions."
The Metropolitan Police is investigating whether Clattenburg used any racist language towards the Chelsea players.