The Jets reportedly wanted Clinkscales to remain a part of the organization, a source told the Daily News.
Last week, NFL Network insider Michael Lombardi reported the Raiders had fired college scouting director Jon Kingdon. The team confirmed the move Tuesday and added that Bruce Kebric also will be relieved of his duties. George Karras and Kent McCloughan will retire, the team announced.
"This was a very difficult decision because these individuals have been part of this organization for all or parts of four decades," McKenzie said in a statement. "We're grateful for their dedicated service to the Raiders."
McKenzie said shortly after taking over as GM in January that he wanted to build his own personnel department after the NFL draft in April. McKenzie is expected to announce the restructuring of the department later this month.
McCloughan, who first joined the organization in the mid-1960s as a standout cornerback, said he still will watch every Raiders game and wished McKenzie the best. McCloughan credited late owner Al Davis for giving him a chance.
"I owe him a lot. He was so nice to my family and me," McCloughan said. "We had some great years, including when Ron Wolf was with us. We won a lot of games. I had the opportunity to work 47 years with one team. I enjoyed it so much. I thought Al Davis was an outstanding person and boss. I enjoyed the scouting department, the coaches and players I had the opportunity to work with, and I'll always be a Raider. I'm going out about as good as a person can go out. You couldn't have written a better story for me."
The Associated Press contributed to this report.