Middleton, 28, became a celebrity after her sister Kate married England's Prince William last April.
Percy, 27, is the future duke of Northumberland.
The pair have known each other since both were students at the University of Edinburgh in Scotland.
Although some British tabloids said last week they started dating this month, two of their friends and a source close to Percy's family are shooting down the romance reports.
"They have always just been friends," a source told Us Weekly. "I don't know how this particular rumor got so out of control! ... Both of them say they are friends and I've not heard or seen anything to suggest otherwise."
"I couldn't imagine them together," a second insider said. "Their friendship is more like brother and sister."
"I wouldn't follow this gossip!" a source close to the Percy family told the magazine.