Over the weekend, Cooper vented his frustration at Deans' tactics and the Australian Rugby Union and said he would like to join friend and All Black Sonny Bill Williams in the National Rugby League.
Reds Chief Executive Carmichael said he would meet the outspoken player and warn him about his damaging comments, the Courier Mail reported.
“I'm fed up to be honest. Quade is making silly comments that do damage to our code,” Carmichael was quoted as saying by the Brisbane newspaper.
The 24-year-old Cooper's error-prone performance after his return from surgery on his right knee earned him Dean's criticism.
The New Zealand-born playmaker has subsequently been injured and will need another operation on the same knee and is doubtful for the Wallabies' tour of Europe where they play England, Italy and Wales in November and early December.
Williams, also New Zealand's heavyweight boxing champion, left the world champion All Blacks and Chiefs for a 12-match deal with Japan's Panasonic Wild Knights and would reportedly join NRL club Sydney Roosters in 2013.